
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
The sequence \(\left\{a_{n}\right\}\) satisfies: \(a_{1}=a_{2}=a_{3}=1\). Let \(b_{n}=a_{n}+a_{n+1}+a_{n+2}\) \((n \in \mathbf{N}^{*})\). If the sequence \(\left\{b_{n}\right\}\) forms a geometric progression with a common ratio of 3, find the value of \(a_{100}\).

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