
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 given arithmetic sequence $\{ a_{n} \}$ satisfies $a_{3} + a_{4} = 4, a_{5} + a_{7} = 6$.

(1) Find the general term formula for $\{ a_{n} \}$.
(2) Let $b_{n} = [a_{n}]$, where $[x]$ denotes the largest integer not greater than $x$. Find the sum of the first 10 terms of the sequence $\{ b_{n} \}$.

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