
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 $f(x)=\sin^4x-\cos^4x$, if the inequality $1+\frac{2}{3}f(x)-mf\left(\frac{x}{2}\right)\geqslant 0$ holds for any $x\in \mathbb{R}$, then the range of the real number $m$ is \_\_\_\_\_\_\_\_\_.

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