
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 Cartesian coordinate system $xOy$, with the origin as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. Suppose points $A$ and $B$ are on the curve $C_{1}$: $\begin{cases} x=3+\cos \theta \\ y=4+\sin \theta \end{cases}$ (with $\theta$ as the parameter) and the curve $C_{2}$: $\rho=1$, respectively. Then, the minimum value of $|AB|$ is \_\_\_\_\_\_.

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