
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Point  $C_{1}$  of hypothenuse  $AC$  of a right-angled triangle  $ABC$  is such that  $BC = CC_{1}$ .  Point  $C_{2}$  on cathetus  $AB$  is such that  $AC_{2} = AC_{1}$ ; point  $A_{2}$  is defined similarly. Find angle  $AMC$ , where  $M$  is the midpoint of  $A_{2}C_{2}$ .

Present the answer in LaTex format: \boxed{Your answer}
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