
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. Suppose points $A$ and $B$ are located on curves $C_{1}$: $ \begin{cases} x=3+2\cos θ \\ y=4+2\sin θ \end{cases}(θ \text{ is the parameter})$ and $C_{2}$: $ρ=1$ respectively. Find the maximum value of $AB$.

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