They are a lot of different actions an army can do. Here below is a list of the most common ones.

Attack actions

Armored Counter-Strike

Assault

Blitz

Breakthrough

Heroic Charge

Human wave

Reversed Front

Shelling

Defence actions

Cleaning Operations

Defensive Withdrawal

Entrenchment

Hedgehog Defence

Secure the Kessel

Supply & Refit actions

Airlift

Ammunition supply

Fuel supply

Refit

Restore Communications

Recon & manoeuvre actions

Behind-the-lines Raids

Deep Raid

Infiltrate

Recon-scouting

Movement actions

Go to the front!

Progress

Strategic Reserve

Air warfare actions

Air Bombardment

Attack Airfields

Air Superiority

Strategic Suppression

Political actions

Barrier Troops

Control by the Party

Nationality Purges

Shoot a traitor!