
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
Observe the following equations:
$$
1^2 = 1, \\
3^2 = 2+3+4, \\
5^2 = 3+4+5+6+7, \\
7^2 = 4+5+6+7+8+9+10, \\
\ldots
$$
From this, we can induce a general equation:
When $n \in \mathbb{N}^*$, $(2n-1)^2 = n + (n+1) + (n+2) + \ldots + \_\_\_\_\_\_$.

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