
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 the polar coordinate system, point $A$ is a moving point on the line $3\rho \cos \theta + 4\rho \sin \theta + 13 = 0$, and point $B$ is a moving point on the curve $\rho + 2\cos \theta = 0$. The minimum value of the distance $|AB|$ is

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