
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
A bank, paying a depositor $p \%$ per annum, in turn, invests the capital at $p_{1} \%$ (of course, $p_{1}>p$). What will be the bank's profit from the entrusted capital \(\boldsymbol{K}\) after \(n\) years, if the interest is compounded annually? Why is the solution: profit \(=K\left(\frac{p_{1}}{100}-\frac{p}{100}\right)^{n}\) incorrect?

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