
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 a right triangle, right at  $B$ , and let  $M$  be the midpoint of the side  $BC$ . Let  $P$  be the point in
bisector of the angle  $ \angle BAC$  such that  $PM$  is perpendicular to  $BC (P$  is outside the triangle  $ABC$ ). Determine the triangle area  $ABC$  if  $PM = 1$  and  $MC = 5$ .

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