
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
A basketball court has a rectangular painting area where the width $x$ of the rectangle must satisfy the equation $16x^2 + 32x - 40 = 0$. The coach wants to rewrite this equation in the form $(ax + b)^2 = c$, where $a$, $b$, and $c$ are integers and $a > 0$. Find the value of $a + b + c$.

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