
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 a right-angled triangle \(15 ABC\) with \(\angle BAC = 90^\circ\), squares \(ABDE\) and \(BCFG\) are constructed on sides \(AB\) and \(BC\) respectively. The area of square \(ABDE\) is \(8 \ \text{cm}^2\) and the area of square \(BCFG\) is \(26 \ \text{cm}^2\). Find the area of triangle \(DBG\) in \(\text{cm}^2\).

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