
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 points $A$, $B$, and $C$ are on the curve $y=\sqrt{x}$ $(x \geqslant 0)$, with x-coordinates $1$, $m$, and $4$ $(1 < m < 4)$, find the value of $m$ that maximizes the area of $\triangle ABC$.

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