
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
The number  $ \left (2+2^{96} \right )!$  has  $2^{93}$  trailing zeroes when expressed in base  $B$ . **a)** Find the minimum possible  $B$ .**b)** Find the maximum possible  $B$ .**c)** Find the total number of possible  $B$ .

*Proposed by Lewis Chen*

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