
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 a dihedral angle $\alpha-l-\beta$ measuring $60^{\circ}$, point $P$ inside the dihedral angle has a distance of 3 to plane $\alpha$ and a distance of 5 to plane $\beta$. If $A \in \alpha$ and $B \in \beta$, find the minimum perimeter of triangle $\triangle PAB$.

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