
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 that the quadrilateral $ABCD$ on a plane is a convex quadrilateral (a convex quadrilateral means that for any side of the quadrilateral, the remaining sides are all on the same side of the line containing that side), and $AB=2$, $BC=4$, $CD=5$, $DA=3$, the maximum area of the quadrilateral $ABCD$ is ______.

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