
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
Alon is solving the equation by completing the square method: $$25x^2 + 30x - 75 = 0.$$ He attempts to rewrite the equation in the form $$(ax + b)^2 = c,$$ where $a$, $b$, and $c$ should be integers and $a > 0$. Find the value of $a + b + c$.

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