
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 function $f(x) = |x - 2| - |2x + 1|.$  
(I) Solve the inequality $f(x) \leq x$ for its solution set;  
(II) If the inequality $f(x) \geq t^2 - t$ holds for all $x \in [-2, -1]$, find the range of the real number $t$.

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