
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
It is known that 
\[
\begin{array}{l}
1 = 1^2 \\
1 + 3 = 2^2 \\
1 + 3 + 5 = 3^2 \\
1 + 3 + 5 + 7 = 4^2
\end{array}
\]
If \(1 + 3 + 5 + \ldots + n = 20^2\), find \(n\).

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