
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 sequences \(\left(x_{n}\right)\) and \(\left(y_{n}\right)\) are given by the formulas \(x_{n}=2n-1\) and \(y_{n}=n^{2}\). If we list all the common terms of these sequences in increasing order, we obtain the sequence \(\left(c_{n}\right)\). Write the formula for the \(n\)-th term of the sequence \(\left(c_{n}\right)\).

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