
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
Define the operation $a*b$ as:
$$
a * b = \begin{cases}
a, & \text{if } a \leq b \\
b, & \text{if } a > b
\end{cases},
$$
for instance, $1 * 2 = 1$. Determine the range of the function $f(x) = 2^x * 2^{-x}$.

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