
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
Suppose in the infinite sequence $\{a\_n\}$ consisting of positive integers, for any positive integer $n$, there is $a\_n \leqslant a_{n+1}$, and for any positive integer $k$, there are exactly $2k-1$ occurrences of $k$ in the sequence. Determine the value of $a_{2014}$.

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