
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
Given the function \( F \) applied to a four-digit positive integer \( \overline{abcd} \), resulting in the integer \( F(\overline{abcd}) = a^4 + b^3 + c^2 + d^1 \). For example, \( F(2019) = 2^4 + 0^3 + 1^2 + 9^1 = 26 \).

Calculate \( F(2019) - F(2018) + F(2017) - \cdots - F(2000) \).

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