
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 $f(x) = |x-a|$, where $a \in \mathbb{R}$.
(I) When $-2 \leq x \leq 3$, the inequality $f(x) \leq 4$ holds. Determine the range of the real number $a$.
(II) If there exists a real number $x$ such that $f(x-a) - f(x+a) \leq 2a - 1$, find the range of the real number $a$.

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