
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 the coordinate plane $xOy$, the angle $\angle MON$ is formed by the ray $y = x$ $(x \geq 0)$ and the positive $x$-axis. Points $A(6, 5)$ and $B(10, 2)$ are two fixed points inside the angle $\angle MON$. Points $P$ and $Q$ are movable points located on the two sides of $\angle MON$. Find the minimum possible value of the perimeter $l$ of the quadrilateral $ABQP$.

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