
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 $f(x) = x^2 - mx + 1$ such that for all real numbers $x$, the inequality $f(x) > 0$ always holds. Additionally, the inequality $x^2 < 9 - m^2$ has a real solution for $x$. If statement (1) is false and statement (2) is correct, determine the range of values for the real number $m$.

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