
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 the function $f(x)$ is an even function defined on $\mathbb{R}$ and is monotonically increasing on the interval $[0,+\infty)$, if the real number $a$ satisfies $f\left( \log_{2}a \right)+f\left( \log_{\frac{1}{2}}a \right)\leqslant 2f\left( 1 \right)$, then the range of the real number $a$ is \_\_\_\_\_\_\_.

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