
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 sequence of real numbers \( a_{n} \) for \( n=1,2,3, \ldots \) is such that \( a_{n+1}=a_{n}+\sqrt{a_{n}+a_{n+1}} \) for \( n=1,2,3, \ldots \) with \( a_{1}=1 \). Find an explicit formula expressing the number \( a_{n} \) in terms of \( n \).

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