
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
The segments \( AP \) and \( AQ \) are tangent to circle \( O \) at points \( P \) and \( Q \), respectively. Moreover, \( QE \) is perpendicular to diameter \( PD \) of length 4. If \( PE = 3.6 \) and \( AP = 6 \), what is the length of \( QE \)?

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