
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
By partial fractions,
\[
\frac{1}{x(x + 1)(x + 2)(x + 3)(x + 4)(x + 5)} = \frac{A}{x} + \frac{B}{x + 1} + \frac{C}{x + 2} + \frac{D}{x + 3} + \frac{E}{x + 4} + \frac{F}{x + 5}
\]
for some constants $A,$ $B,$ $C,$ $D,$ $E,$ and $F.$ Find $A + B + C + D + E + F.$

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