
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
Between two consecutive perfect squares $y$ and $z$, a new term is defined as the average of these squares, added to the square root of the first square. Let $y = n^2$ and $z = m^2$, where $n = k$ and $m = k+1$. What is this new term?
A) $n^2 + 2n\qquad$ B) $n^2 + 2n + 1\qquad$ C) $n^2 + 2n + 0.5\qquad$ D) $n^2 + n + 1\qquad$ E) $n^2 + n + 0.5$

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