
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 parametric equations of curve C as follows:
$$
\begin{cases}
x = 2 + \sqrt{5} \cos \alpha \\
y = 1 + \sqrt{5} \sin \alpha
\end{cases}
$$
where $\alpha$ is the parameter. Establish a polar coordinate system with the origin of the rectangular coordinate system as the pole and the positive half of the Ox axis as the polar axis.

1. Find the polar equation of curve C.
2. If the polar equation of line l is $\rho(\sin \theta + \cos \theta) = 1$, find the length of the chord intercepted by line l on curve C.

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