
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 a circle passing through the origin \\(O\\) with the equation \\(x^{2}+y^{2}-2ax=0\\) and also passing through the point \\((4,2)\\), \\((1)\\) find the equation of the circle, \\((2)\\) let \\(A\\) be a moving point on the circle, find the equation of the trajectory of the midpoint \\(M\\) of chord \\(OA\\).

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