
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: $$x=3+\sqrt{10}\cos\alpha$$ and $$y=1+\sqrt{10}\sin\alpha$$, where $\alpha$ is a parameter. Establish a polar coordinate system with the origin O of the rectangular coordinate system as the pole and the positive half of the x-axis as the polar axis.

(1) Find the polar equation of curve C and explain what trajectory it represents;

(2) If the polar equation of a straight line is given by $$\sin\theta - \cos\theta = \frac{1}{\rho}$$, find the length of the chord cut by curve C.

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