
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
Let \( f(x) \) be the polynomial \( (x - a_1)(x - a_2)(x - a_3)(x - a_4)(x - a_5) \) where \( a_1, a_2, a_3, a_4, \) and \( a_5 \) are distinct integers. Given that \( f(104) = 2012 \), evaluate \( a_1 + a_2 + a_3 + a_4 + a_5 \).

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