
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 $f(x) = e^{x} - \frac{1}{e^{x}} + x$, where $e$ is the base of the natural logarithm, if the real number $a$ satisfies $f(\log_{2}a) - f(\log_{0.5}a) \leqslant 2f(1)$, determine the range of values for $a$.

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