
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
An arbitrary quadrilateral is divided by its diagonals into four triangles; the areas of three of them are 10, 20, and 30, each being smaller than the area of the fourth triangle. Find the area of the given quadrilateral.

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