
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
Given a triangle \( ABC \). A line parallel to \( AC \) intersects sides \( AB \) and \( BC \) at points \( P \) and \( T \) respectively, and the median \( AM \) at point \( Q \). It is known that \( PQ = 3 \) and \( QT = 5 \). Find the length of \( AC \).

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