
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 a cubic function $f(x) = x^3 + ax^2 - 6x + b$, where $a$ and $b$ are real numbers, and $f(0) = 1$. The slope of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ is $-6$.  
(1) Find the analytical expression of the function $f(x)$.  
(2) If $f(x) \leq |2m-1|$ holds for any $x \in (-2, 2)$, find the range of the real number $m$.

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