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

(1) Find the general term formula for $\{{a_{n}}\}$.

(2) Let ${{b}_{n}}=[{{a}_{n}}]$, where $[x]$ denotes the greatest integer not exceeding $x$. Find the sum of the first 10 terms of the sequence $\{{{b}_{n}}\}$.

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