
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
If the initial sides of a triangle are \(a\) and \(b\) with included angle \(\theta\), determine the factor by which the area is multiplied when one side is tripled and the other side is doubled.

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