ausarbeiten
to work out
To develop and create a plan, concept, text, or idea in detail and with care.
Das Team hat eine umfassende Strategie für das neue Projekt ausgearbeitet.
The team worked out a comprehensive strategy for the new project.

to work out / elaborate
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to work out
To develop and create a plan, concept, text, or idea in detail and with care.
Das Team hat eine umfassende Strategie für das neue Projekt ausgearbeitet.
The team worked out a comprehensive strategy for the new project.

'Ausarbeiten' (to work out/elaborate) is a separable verb. The prefix 'aus-' goes at the end in a main clause, remains attached to the verb in subordinate clauses, and in the infinitive with 'zu', 'zu' stands between 'aus' and 'arbeiten'.
Die Architektin arbeitet den Bauplan detailliert aus.
The architect works out the building plan in detail.
The verb is made up of the prefix 'aus-' and the verb 'arbeiten' (to work). Here, the prefix 'aus-' emphasizes that something is thought through or completed fully, in detail, and to the end.
Wir müssen die Präsentation bis morgen fertig ausarbeiten.
We have to finish working out the presentation by tomorrow.
In the meaning 'entwickeln' (to develop), 'ausarbeiten' (to work out) is often used with abstract concepts. Typical combinations are: 'einen Plan ausarbeiten' (to work out a plan), 'ein Konzept ausarbeiten' (to work out a concept), 'einen Vertrag ausarbeiten' (to draft a contract), or 'eine Rede ausarbeiten' (to prepare a speech in detail).
Die Anwälte haben den Vertrag gemeinsam ausgearbeitet.
The lawyers worked out the contract together.
When it is about craft or artistic shaping, the material from which something is made is often mentioned. Pay attention to the preposition 'aus' followed by a material in the dative.
Der Künstler arbeitete die feinen Gesichtszüge aus dem Marmorblock aus.
The artist carved the fine facial features out of the block of marble.
to work
'arbeiten an' and 'ausarbeiten' can both be used with plans, texts, concepts, or ideas. 'arbeiten an' only says that you are dealing with something and continuing to work on it. 'ausarbeiten' is more specific: you develop something carefully, clarify details, and bring it into a finished or nearly finished form. The words can be confused because both involve working toward a result. If you only mean the process, 'arbeiten an' is more natural. If you mean developing something in detail and finishing it, 'ausarbeiten' fits better.

Meine Freundin arbeitet ein genaues Konzept für das Schulfest aus.
My friend is working out a detailed concept for the school festival.
Nach der Besprechung arbeiten wir weiter an dem Reiseplan.
After the meeting, we continue working on the travel plan.