
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
Find the integer $b$ for which the equation
\[
\sqrt[a]{N\sqrt[b]{N\sqrt[c]{N^2}}} = \sqrt[24]{N^{17}}
\]
holds true for all $N \neq 1$, where $a, b, c$ are integers greater than 1.
- **A)** 2
- **B)** 3
- **C)** 4
- **D)** 5
- **E)** 6

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