
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 $xOy$, a polar coordinate system is established with $O$ as the pole and the positive half-axis of the $x$-axis as the polar axis. It is given that point $A$ is on the curve $C_1$ and point $B$ is on the curve $C_2$, where $C_1$ is described by the equations:
\[
\begin{cases}
x=3+\cos θ, \\
y=4+\sin θ,
\end{cases}
\]
($θ$ is the parameter) and $C_2$ is described by the polar coordinate equation $\rho=1$. Find the minimum value of the length of segment $AB$.

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