
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 $f(x) = |2x-1| + |x+1|$.

(Ⅰ) Solve the inequality: $f(x) \leqslant 2$;

(Ⅱ) If for $\forall x \in \mathbb{R}$, $\exists a \in [-2,1]$ such that $f(x) \geqslant f(a) + m$ holds, find the range of the real number $m$.

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