
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 on the curve $\rho + 2\cos\theta = 0$, and point $B$ is on the line $\begin{cases} & x = -3 + 4t \\ & y = -1 - 3t \end{cases}$. Find the minimum value of the distance $|AB|$.

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