
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
In the sequence $\{a_n\}$, $a_n = 1^1 + 2^2 + 3^3 + \ldots + n^n$, where $n \in \mathbb{N^{*}}$. In the sequence $\{b_n\}$, $b_n = \cos(a_n \pi)$, where $n \in \mathbb{N^{*}}$. Find the value of $b_{2008} - b_{2009}$.

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