
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 \(\left\{a_{n}\right\}\) be a given sequence. If \(b_{n} = \sum_{k=0}^{n}(-1)^{k} \binom{n}{k} a_{k}\) for \(n = 0, 1, 2, \ldots\), then \(a_{n} = \sum_{k=0}^{n}(-1)^{k} \binom{n}{k} b_{k}\) for \(n = 0, 1, 2, \ldots\).

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