
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
For any sequence \(A\): \(a_{1}\), \(a_{2}\), \(a_{3}\), \(\ldots\), \(a_{n}\), \(\ldots\), define \(\Delta A\) as the sequence \(a_{2}-a_{1}\), \(a_{3}-a_{2}\), \(a_{4}-a_{3}\), \(\ldots\), \(a_{n+1}-a_{n}\), \(\ldots\). If for sequence \(A\) all terms of the sequence \(\Delta (\Delta A)\) are equal to \(1\), and \(a_{12}=a_{22}=0\), then find \(a_{2}\).

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