
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 $f(x) = |x + 3| + |x - a|$ ($a > 0$).

(1) When $a = 4$, and it is known that $f(x) = 7$, find the range of $x$.

(2) If the solution set of $f(x) \geq 6$ is $\{x | x \leq -4 \text{ or } x \geq 2\}$, find the value of $a$.

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