
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
In the rectangular coordinate system $xOy$, a rhombus $OABC$ has its diagonals intersecting at point $M(x_{0}, y_{0})$. The hyperbola $y = \frac{k}{x}$ (where $x > 0$) passes through points $C$ and $M$. If $2 \leqslant x_{0} \leqslant 4$, then what is the maximum area of the rhombus $OABC$?

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