
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 of real numbers $A=\{a_1, a_2, a_3, \ldots\}$, define $\triangle A$ as the sequence $\{a_2 - a_1, a_3 - a_2, a_4 - a_3, \ldots\}$, where the $n$-th term is $a_{n+1} - a_n$. Assume that all terms of the sequence $\triangle (\triangle A)$ are $1$ and $a_{18} = a_{2017} = 0$, find the value of $a_{2018}$.

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