
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 $f(x) = x^2 - 2x + 3$.

$(1)$ Is there a real number $m$ such that the inequality $m + f(x) > 0$ holds for any $x \in \mathbb{R}$? Explain your reasoning.

$(2)$ If there exists a real number $x$ such that the inequality $m - f(x) > 0$ holds, find the range of values for the real number $m$.

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