
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
Let  $ABC$  be an isosceles right triangle at  $A$  with  $AB=AC$ . Let  $M$  and  $N$  be on side  $BC$ , with  $M$  between  $B$  and  $N,$  such that   $$ BM^2+ NC^2= MN^2. $$   Determine the measure of the angle  $\angle MAN.$ 

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