
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 $f(x) = |x - m|$, the solution set for the inequality $f(x) \leq 3$ is $[-1, 5]$.
(1) Determine the value of the real number $m$;
(2) Given that $a, b, c \in \mathbb{R}$, and $a - 2b + 2c = m$, find the minimum value of $a^2 + b^2 + c^2$.

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