
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
The function $y=f(x)$ satisfies $f(3+x)=f(1-x)$, and for $x_1, x_2 \in (2, +\infty)$, the inequality $$\frac{f(x_1)-f(x_2)}{x_1-x_2} > 0$$ holds. If $f(\cos^2\theta+2m^2+2) < f(\sin\theta+m^2-3m-2)$ always holds for $\theta \in \mathbb{R}$,  
(1) Determine the monotonicity and symmetry of $y=f(x)$;  
(2) Find the range of values for $m$.

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