
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 triangle \(XYZ\), \(YZ = 30\) and \(\angle Y = 60^\circ\). Let the perpendicular bisector of \(YZ\) intersect \(YZ\) and \(XZ\) at \(P\) and \(Q\), respectively. Find the length of \(PQ\).

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