
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
Given line $l$: $\frac{x}{4} + \frac{y}{3} = 1$, $M$ is a moving point on $l$, and the perpendiculars from $M$ to the $x$-axis and $y$-axis intersect at points $A$ and $B$, respectively. Point $P$ lies on the line segment $AB$ such that $\overrightarrow{AP} = 2\overrightarrow{PB}$. Find the locus equation of point $P$.

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