
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
Assume that  $f(a+b) = f(a) + f(b) + ab$ , and that  $f(75) - f(51) = 1230$ .  Find  $f(100)$ .

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