mäßigen
to moderate
To reduce or dampen the intensity, extent, or speed of something.
Der Arzt riet ihm, seinen Alkoholkonsum zu mäßigen.
The doctor advised him to moderate his alcohol consumption.

to moderate / restrain
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to moderate
To reduce or dampen the intensity, extent, or speed of something.
Der Arzt riet ihm, seinen Alkoholkonsum zu mäßigen.
The doctor advised him to moderate his alcohol consumption.

The verb 'mäßigen' (to moderate/restrain) belongs to the word family of 'das Maß' (measure) and the adjective 'mäßig' (moderate). Literally, it means bringing something to a healthy or appropriate 'Maß' (measure).
Versuche, deinen Kaffeekonsum ein wenig zu mäßigen.
Try to moderate your coffee consumption a little.
The meaning depends on how it is used. Without a reflexive pronoun, it means reducing an external thing ('das Tempo mäßigen' — to moderate the pace). With a reflexive pronoun ('sich mäßigen' — to restrain oneself), it means controlling one's own behavior.
Der Redner wurde gebeten, seine Lautstärke zu mäßigen.
The speaker was asked to moderate his volume.
You can 'mäßigen' (moderate) abstract things or behaviors. Typical combinations are 'das Tempo mäßigen' (to moderate the pace), 'den Alkoholkonsum mäßigen' (to moderate alcohol consumption), or 'seine Begeisterung mäßigen' (to moderate one's enthusiasm).
Bitte mäßigen Sie Ihre Geschwindigkeit in der Spielstraße.
Please moderate your speed in the traffic-calmed street.
When a person is supposed to hold themselves back, the verb is used reflexively: 'sich mäßigen' (to restrain oneself). The reflexive pronoun is in the accusative.
Der Trainer sagte dem Spieler, er solle sich in seiner Kritik am Schiedsrichter mäßigen.
The coach told the player that he should restrain himself in his criticism of the referee.
to reduce
'reduzieren' and 'mäßigen' both mean that something becomes less strong or less large. 'reduzieren' is more general and works well with amounts, costs, times, or numbers. 'mäßigen' is used more when something is too strong, too fast, or too intense and should become calmer. As a reflexive verb, 'sich mäßigen' means that a person restrains themselves, for example when eating, speaking, or arguing. 'reduzieren' sounds more factual, while 'mäßigen' has a stronger sense of control and restraint.

Nach dem Streit mäßigt Paul seinen Ton und spricht ruhiger.
After the argument, Paul moderates his tone and speaks more calmly.
Luisa hat beim Termin ihre Arbeitszeit reduziert.
Luisa reduced her working hours during the appointment.