
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 that \( c \) is a positive integer not exceeding 2017, and there exist positive integers \( a \) and \( b \) such that
\[ 
2^{a} \times 5^{b} = \left(a^{3} + a^{2} + a + 1\right) c, 
\]
find the maximum value of \( c \).

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