
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
Points  $M$ ,  $N$ ,  $P$  are selected on sides  $\overline{AB}$ ,  $\overline{AC}$ ,  $\overline{BC}$ , respectively, of triangle  $ABC$ .  Find the area of triangle  $MNP$  given that  $AM=MB=BP=15$  and  $AN=NC=CP=25$ .

*Proposed by Evan Chen*

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