
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 ${{a_{3}}+{{a_{4}}=4,{{a}_{5}}+{{a}_{7}}=6}}$.

(I) Find the general term formula for $\{{{a_{n}}}\}$;

(II) Let ${{b_{n}}=[{{a_{n}}]}}$, find the sum of the first 10 terms of the sequence $\{{{b_{n}}}\}$, where $[x]$ denotes the largest integer not greater than $x$, e.g., $[0.9]=0$, $[2.6]=2$.

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