
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 $f(x) = |x - a| + |x + 2|$ (where $a$ is a constant and $a\in\mathbb{R}$):  
(i) If the minimum value of the function $f(x)$ is $2$, find the value of $a$;  
(ii) When $a = 2$, solve the inequality $f(x) \leq 6$.

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