
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 graph of the power function $f(x)$ passes through the point $(\sqrt{3}, 3)$. If the function $g(x) = f(x) + 1$ has a range of $[1, 5]$ on the interval $[m, 2]$, then the range of the real number $m$ is ______.

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