
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
In square  $ABCD$  with side length  $2$ , let  $M$  be the midpoint of  $AB$ . Let  $N$  be a point on  $AD$  such that  $AN = 2ND$ . Let point  $P$  be the intersection of segment  $MN$  and diagonal  $AC$ . Find the area of triangle  $BPM$ .

*Proposed by Jacob Xu*

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