
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
$ABCDE$ is a regular pentagon. $AP$, $AQ$, and $AR$ are the perpendiculars dropped from $A$ onto $CD$, $BC$ extended, and $DE$ extended, respectively. Let $O$ be the center of the pentagon. If $OP = 2$, then find $AO + AQ + AR$.

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