
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
Line \( l_1 \) passes through the point \( P(3, 2) \) and has an inclination angle of \( \arctan \frac{3}{4} \). If \( l_1 \) intersects line \( l_2: x - 2y + 11 = 0 \) at point \( Q \), find the distance \( |PQ| \).

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