
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 $\{a_n\}$, $a_3+a_4=4$, $a_5+a_7=6$.  
(I) Find the general formula for $\{a_n\}$.  
(II) Let $b_n=\lfloor a_n \rfloor$, calculate the sum of the first $10$ terms of the sequence $\{b_n\}$, where $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$, such as $\lfloor 0.9 \rfloor=0$, $\lfloor 2.6 \rfloor=2$.

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