
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
Given that the polar coordinate equation of curve $C$ is $ρ=4\sin(θ-\frac{π}{3})$, with the pole as the origin and the polar axis as the positive half of the $x$-axis, establish a rectangular coordinate system $xOy$.

1. Find the rectangular coordinate equation of curve $C$;
2. If point $P$ is on curve $C$, and point $Q$ has rectangular coordinates $(\cos φ,\sin φ)$, where $(φ∈R)$, find the maximum value of $|PQ|$.

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