
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
Define the operation \( a * b = ab - 5 \left\lfloor \frac{ab}{5} \right\rfloor \), where \(\left\lfloor x \right\rfloor\) represents the greatest integer less than or equal to the real number \( x \). Given the set \( A = \{0, 1, 2, 3, 4\} \), and a bijection \( f: A \rightarrow A \) such that \( f(a * b) = f(a) * f(b) \), find the number of functions \( f \) that satisfy the condition.


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