
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 $\triangle ABC$, the base $BC = 2$ and the height $AD = 1$. Let $M$ be any point on $BC$. Draw $MN // AC$ intersecting $AB$ at $N$, and draw $MP // AB$ intersecting $AC$ at $P$. Find the position of point $M$ such that the area of $\triangle MNP$ is maximized.

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