
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
Suppose
\[
\frac{1}{x^4 - 20x^3 + 147x^2 - 490x + 588} = \frac{A}{x+3} + \frac{B}{x-4} + \frac{C}{(x-4)^2} + \frac{D}{(x-7)}
\]
where $A$, $B$, $C$, and $D$ are constants. What is the value of $A$?

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