
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 equilateral triangle  $ABC$  is divided by nine lines parallel to  $BC$  into ten bands that are equally wide. We colour the bands alternately red and blue, with the smallest band coloured red. The difference between the total area in red and the total area in blue is  $20$   $\text{cm}^2$ .

What is the area of triangle  $ABC$ ?

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