
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
In a triangle \(PQR\), point \(Z\) lies on segment \(PR\) such that \(\angle QZP = \angle QZR\). Given \(PZ = 18\) units, \(QR = 42\) units, and \(RZ = 36\) units, find the length of \(QZ\).

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