
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
Let \\(P\\) be a point on the curve \\(C\\): \\(y=x^{2}-2x+3\\), and the range of the slope angle of the tangent line at point \\(P\\) on curve \\(C\\) is \\(\left[0, \frac{\pi}{4}\right]\\). Find the range of the x-coordinate of point \\(P\\.

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