
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 $f(x)\leqslant 6$ is $\{-2\leqslant x\leqslant 3\}$, find the value of the real number $a$.
2. Under the condition of (1), if there exists a real number $t$ such that $f(\frac{t}{2})\leqslant m-f(-t)$ holds, find the range of values of the real number $m$.

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