
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 $f(x) = |2x-a| + a$.
(1) If the solution set of the inequality $f(x) \leq 6$ is $\{x|-2 \leq x \leq 3\}$, find the value of the real number $a$;
(2) Under the condition of (1), if there exists a real number $t$ such that $f\left( \frac{t}{2} \right) \leq m - f(-t)$ holds, find the range of the real number $m$.

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