
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 triangle with area  $1$  and  $P$  the middle of the side   $[BC]$ .  $M$  and  $N$  are two points of  $[AB]-\left \{ A,B \right \} $  and  $[AC]-\left \{ A,C \right \}$  respectively such that  $AM=2MB$  and $CN=2AN$ .  The two lines  $(AP)$  and  $(MN)$  intersect in a point  $D$ . Find the area of the triangle  $ADN$ .

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