
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) \( a^5 - a \) is divisible by 30;

b) \( a^{17} - a \) is divisible by 510;

c) \( a^{11} - a \) is divisible by 66;

d) \( a^{73} - a \) is divisible by \( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 19 \cdot 37 \cdot 73 \).

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