
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 $f(x) = m - |x - 2|$, the solution set of the inequality $f(x + 2) \geq 0$ is $[-2, 2]$.  
(1) Find the value of $m$;  
(2) If for all $x \in \mathbb{R}$, $f(x) \geq -|x + 6| - t^2 + t$ always holds, find the range of the real number $t$.

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