
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 the function $f(x)=x-2\sin x$,  
(Ⅰ) Find the maximum and minimum values of $f(x)$ on the interval $[0,\pi]$.  
(Ⅱ) If there exists $x \in (0, \frac{\pi}{2})$ such that the inequality $f(x) < ax$ holds, determine the range of the real number $a$.

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