sich etwas vornehmen
to plan to do
To make a firm plan or form the intention to do something specific.
Für das neue Jahr habe ich mir vorgenommen, mehr Sport zu treiben.
For the new year, I've planned to do more sports.

to plan / carry out
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to plan to do
To make a firm plan or form the intention to do something specific.
Für das neue Jahr habe ich mir vorgenommen, mehr Sport zu treiben.
For the new year, I've planned to do more sports.

'Vornehmen' (to plan / carry out) is a separable verb. The prefix 'vor' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich nehme mir für morgen nicht zu viel vor.
I'm not planning too much for tomorrow.
When making a plan, the construction is reflexive: 'sich (Dativ) etwas vornehmen' (to plan something for oneself). It is often followed by an infinitive clause with 'zu'.
Ich habe mir vorgenommen, jeden Tag Deutsch zu lernen.
I've planned to study German every day.
In this meaning, 'vornehmen' (to carry out) is rather formal and is often used in official or technical contexts. Typical objects are abstract nouns like 'Änderungen' (changes), 'Anpassungen' (adjustments), or 'eine Messung' (a measurement).
Der Gutachter wird eine genaue Prüfung des Gebäudes vornehmen.
The assessor will carry out a precise inspection of the building.
to plan
'planen' and 'sich etwas vornehmen' both have to do with intentions for the future. However, 'planen' puts more emphasis on organization: you think about when, how, and with whom something should happen. 'sich etwas vornehmen' is more about making a firm personal decision. Learners may confuse the words because both talk about future actions. As a simple guide: you set yourself a goal with 'sich etwas vornehmen', but you plan the exact steps with 'planen'.

Zu Hause nehme ich mir vor, am nächsten Tag endlich aufzuräumen.
At home, I resolve to finally clean up the next day.
Die Fahrerin hat geplant, morgen früher zur Arbeit zu fahren.
The driver has planned to leave for work earlier tomorrow.