
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
Let \(P\) be a point not on line \(XZ\) and \(Q\) a point on line \(XZ\) such that \(PQ \perp XZ\). Meanwhile, \(R\) is a point on line \(PX\) such that \(XR \perp PX\). If \(XR = 3\), \(PQ = 6\), and \(XZ = 7\), then what is the length of \(PX\)?

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