
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 $xOy$, a pole coordinate system is established with the coordinate origin $O$ as the pole and the $x$-axis as the polar axis. The parametric equation of the curve $C_1$ is $$\begin{cases} x=2+2\cos\alpha \\ y=2\sin\alpha \end{cases}$$ (where $\alpha$ is the parameter).

1. Find the general equation (in standard form) and the polar coordinate equation of $C_1$.
2. The polar coordinate equation of the curve $C_2$ is $\rho = \frac{4\cos\theta}{1-\cos2\theta}$ ($-\frac{\pi}{2} \leq \theta \leq \frac{\pi}{2}$, and $\theta \neq 0$). $C_1$ and $C_2$ intersect at a point $A$ (different from $O$). Find $|OA|$.

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