
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 equilateral triangle.  $N$  is a point on the  side  $AC$  such that  $\vec{AC} = 7\vec{AN}$ ,  $M$  is a point on the side   $AB$   such that  $MN$  is parallel to  $BC$  and  $P$  is a point on the side  $BC$   such that  $MP$  is parallel to  $AC$ . Find the ratio of areas  $\frac{ (MNP)}{(ABC)}$ 

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