
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 rectangular coordinate system $Oy$, establish a polar coordinate system with the origin as the pole and the positive semi-axis as the polar axis. Suppose points $A$ and $B$ are located on the curves $C_1$: $\begin{cases} x=3+\cos \theta, \\ y=4+\sin \theta \end{cases}$ ($\theta$ is the parameter) and $C_2$: $\rho=1$, respectively. The minimum value of $|AB|$ is ________.

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