
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 $f(x) = x^2$ and $g(x) = (\frac{1}{2})^x - m$, find the range of the real number $m$ such that for every $x_1 \in [-1, 3]$, there exists $x_2 \in [0, 2]$ satisfying $f(x_1) \geq g(x_2)$.

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