
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 the maximum value of the function $f(x)= \sqrt {x-2}+ \sqrt {11-x}$ be $M$.
(I) Find the value of the real number $M$;
(II) Find the solution set of the inequality $|x- \sqrt {2}|+|x+2 \sqrt {2}|\leqslant M$.

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