
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 $O$ as the pole and the positive semi-axis of the $x$-axis as the polar axis. In the polar coordinate system, let point $P$ be any point on the curve $C_1: p = 2 \cos \theta$, and point $Q$ lies on the ray $OP$ such that $|OP| \cdot |OQ| = 6$. Denote the locus of point $Q$ as $C_2$.

(1) Find the rectangular coordinate equation of curve $C_2$;

(2) Line $l: \theta = \frac{π}{3}$ intersects $C_1$ and $C_2$ at points $A$ and $B$, respectively. Find $|AB|$.

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