
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 $xOy$, line $l$ passes through point $P(0, m)$ with an inclination angle of $45^\circ$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. The curve $C$ is defined as: $\rho^2 - 2\rho\cos\theta - 1 = 0$.
(1) Find the rectangular coordinate equation of curve $C$.
(2) Suppose line $l$ intersects curve $C$ at points $A$ and $B$, and $|PA|\cdot|PB| = 2$. Find the rectangular coordinate equation of line $l$.

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