
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
(For this question, the full score is 10 points) Elective 4-5: Special Topics on Inequalities

Given the function $f(x) = |x - a| + |x + 2|$ (where $a$ is a constant and $a \in \mathbb{R}$);

(1) When $a = 1$, solve the inequality $f(x) \leq 5$;

(2) When $a \geq 1$, find the range of the function $f(x)$.

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