
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 $f(x) = 2\sin^2(\omega x + \frac{\pi}{4}) - \sqrt{3}\cos(2\omega x)$, where $\omega > 0$, has a period of $\pi$.
1. Find $\omega$ and the range of the function $f(x)$.
2. If the inequality $|f(x) - m| < 2$ always holds for $x \in \left[\frac{\pi}{4}, \frac{\pi}{2}\right]$, find the range of the real number $m$.

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