
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 that $A$, $B$, and $C$ are the three interior angles of $\triangle ABC$, let $f(B)=4\sin B\cdot\cos^2\left(\frac{\pi}{4}-\frac{B}{2}\right)+\cos 2B$. Find the range of the real number $m$ for which $f(B)-m < 2$ always holds.

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