
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 arithmetic sequence $\{a\_n\}$, it is given that $a\_3 + a\_4 = 12$ and $S\_7 = 49$.
(I) Find the general term formula for the sequence $\{a\_n\}$.
(II) Let $[x]$ denote the greatest integer not exceeding $x$, for example, $[0.9] = 0$ and $[2.6] = 2$. Define a new sequence $\{b\_n\}$ where $b\_n = [\log_{10} a\_n]$. Find the sum of the first 2000 terms of the sequence $\{b\_n\}$.

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