
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 the line $x+2y-4=0$ intersects the parametric equations $\begin{cases} \left.\begin{matrix}x=2-3\cos\theta \\ y=1+3\sin\theta\end{matrix}\right\} \end{cases}$ ($\theta$ is the parameter) at points A and B, find the length of $|AB|$.

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