
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 \\(k \in \mathbb{R}\\), the line \\(l_1\\): \\(kx+y=0\\) passes through a fixed point \\(P\\), and the line \\(l_2\\): \\(kx-y-2k+2=0\\) passes through a fixed point \\(Q\\). If a moving point \\(M\\) is on the circle with diameter \\(PQ\\), find the maximum value of \\(|MP|+|MQ|\\).

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