
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
A moving point \\(M\\) is at the same distance from the line \\(l\\): \\(x=-1\\) as it is from the fixed point \\(F(1,0)\\).

\\((1)\\) Find the equation of the trajectory \\(C\\) of point \\(M\\);

\\((2)\\) Find the length of the chord \\(AB\\) with \\(P(2,1)\\) as its midpoint.

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