
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
$n$ is a positive integer. Let $a_{n}$ be the integer closest to $\sqrt{n}$, and let $b_{n} = n + a_{n}$. Remove $b_{n}$ from the set of all positive integers, and arrange the remaining positive integers in ascending order to form the sequence $\left\{c_{n}\right\}$. Express $c_{n}$ in terms of $n$.

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