
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
Scalene triangle \(PQR\) has \(PQ = 6\), \(PR = 7\), and \(QR = 8\). Right triangle \(ABC\) (hypotenuse \(\overline{AB}\)) is inscribed such that \(B\) is on \(PR\), \(C\) is on \(QR\), and \(A\) is on \(PQ\). Given \(PC = 4\) and \(BP = CQ = 3\), compute \(AQ\).

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