
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
$$
f(x)=2 \sin ^{2}\left(\frac{\pi}{4}-x\right)-\sqrt{3} \cos 2 x.
$$
(1) Find the smallest positive period and the interval of monotonic decrease of \( f(x) \).

(2) If \( f(x) < m + 2 \) is always true for \( x \in \left[0, \frac{\pi}{6} \right] \), determine the range of values for the real number \( m \).

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