
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
If the first term of the sequence \\(\\{a\_n}\\) is \\(a\_1=2\\) and \\(a\_{n+1}=3a\_n+2\\) for all \\(n\in\mathbb{N}^*\\), and we define \\(b\_n=\log\_3(a\_n+1)\\), then what is the value of \\(b\_1+b\_2+b\_3+ \cdots +b\_{100}=\\)?

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