
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 $f(x) = x^3 - 3x + m$, with three numbers $a$, $b$, $c$ chosen from the interval $[0, 2]$, determine the range of values for $m$ such that there exists a triangle with side lengths $f(a)$, $f(b)$, $f(c)$.

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