
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
For integers \(a, b, c, d\), let \(f(a, b, c, d)\) denote the number of ordered pairs of integers \((x, y) \in \{1,2,3,4,5\}^{2}\) such that \(ax + by\) and \(cx + dy\) are both divisible by 5. Find the sum of all possible values of \(f(a, b, c, d)\).

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