
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 \( \triangle ABC \), \( AB = 8 \), \( BC = 11 \), and \( AC = 6 \). The points \( P \) and \( Q \) are on \( BC \) such that \( \triangle PBA \) and \( \triangle QAC \) are each similar to \( \triangle ABC \). What is the length of \( PQ \)?

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