
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
The area of triangle \(ABC\) is \(30 \text{ cm}^2\). Point \(D\) is taken on side \(AC\) such that \(AD:DC = 2:3\). The length of the perpendicular \(DE\) dropped to side \(BC\) is \(9 \text{ cm}\). Find \(BC\).

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