
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
Let the function $f(x) = 2^{x+\cos\alpha} - 2^{-x+\cos\alpha}$, where $x \in \mathbb{R}$, and $f(1) = \frac{3}{4}$.

(1) Find the set of values for $\alpha$;  
(2) If for $0 \leq \theta \leq \frac{\pi}{2}$, $f(m\cos\theta) + f(1-m) > 0$ always holds, find the range of values for the real number $m$.

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