
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 that $P$ and $Q$ are two points on the unit circle centered at the origin $O$, and they are located in the first and fourth quadrants, respectively. The $x$-coordinate of point $P$ is $\frac{4}{5}$, and the $x$-coordinate of point $Q$ is $\frac{5}{13}$. Then, $\cos \angle POQ=$ ______.

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