
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 that the quadratic function \( f(x) \) has a maximum value of 12 on the interval \([-1,4]\) and the solution set of the inequality \( f(x) < 0 \) is \((0,5)\),
1. Find the expression for the function \( f(x) \).
2. If for any \( x \in \mathbf{R} \), the inequality \( f(2-2 \cos x) < f(1 - \cos x - m) \) is always satisfied, determine the range of the real number \( m \).

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