
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 Cartesian coordinate system $xOy$, the parametric equations of curve $C$ are $\left\{\begin{array}{l}{x=2-t-{t}^{2},}\\{y=2-3t+{t}^{2}}\end{array}\right.$ (where $t$ is a parameter and $t\neq 1$). Curve $C$ intersects the coordinate axes at points $A$ and $B$. <br/>$(1)$ Find $|AB|$;<br/>$(2)$ Establish a polar coordinate system with the origin as the pole and the positive $x$-axis as the polar axis. Find the polar coordinate equation of the line $AB$.

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