
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
Find the value of the expression \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\), given that \(a, b, c\) are three distinct real numbers satisfying the equations:

\[a^3 - 2020a + 1010 = 0,\]
\[b^3 - 2020b + 1010 = 0,\]
\[c^3 - 2020c + 1010 = 0.\]

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