
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 $xOy$, establish a polar coordinate system with the origin as the pole and the positive semi-axis of $x$ as the polar axis. Let points $A$ and $B$ be located on curves $C\_1$ and $C\_2$ respectively.

Curve $C\_1$ is defined by the parametric equations:
\[
\begin{cases}
x = 3 + 2\cos\theta, \\
y = 4 + 2\sin\theta
\end{cases}
\]
where $\theta$ is a parameter.

Curve $C\_2$ is defined by the polar equation:
\[
\rho = 1
\]

(1) Convert the parametric equation of curve $C\_1$ and the polar equation of curve $C\_2$ into Cartesian equations.

(2) Find the maximum value of $AB$.

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