
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
The polar equation of curve C<sub>1</sub> is $\rho=4\cos\theta$, and the parametric equation of line C<sub>2</sub> is
$$\begin{cases} x=3+4t \\ y=2+3t\end{cases} \quad (t\text{ is the parameter}).$$
(1) Convert C<sub>1</sub> into a Cartesian coordinate equation.
(2) Do C<sub>1</sub> and C<sub>2</sub> intersect? If they intersect, find the length of the chord; if not, explain why.

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