
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

Let squares of one kind have a side of \(a\) units, another kind have a side of \(b\) units, and the original square have a side of \(c\) units. Then the area of the original square is given by \(c^{2}=n a^{2}+n b^{2}\).

Numbers satisfying this equation can be obtained by multiplying the equality \(5^{2}=4^{2}+3^{2}\) by \(n=k^{2}\). For \(n=9\), we get \(a=4, b=3, c=15\).

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