
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 $\\{a_{n}\\}$, $a_{1}=1$, $a_{6}=3$

(1) Find the general formula for $\\{a_{n}\\}$;
(2) Let $b_{n}=[a_{n}]$, find the sum of the first 5 terms in the sequence $\\{b_{n}\\}$, where $[x]$ represents the greatest integer not exceeding $x$, e.g. $[0.9]=0$, $[2.6]=2$

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