
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
Consider the function $f(x) = \sin x - \cos x + x + 1$.
(I) For $x \in [0, 2\pi]$, determine the monotonic intervals and the extreme values of $f(x)$;
(II) If the function $y = f(x) - ax$ is increasing on $[0, \pi]$, find the range of the real number $a$.

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