
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 real number sequence $A=\left\{ {{a}_{1}},{{a}_{2}},{{a}_{3}},\cdots \right\}$, define $\Delta A$ as the sequence $\left\{ {{a}_{2}}-{{a}_{1}},{{a}_{3}}-{{a}_{2}},{{a}_{4}}-a{}_{3}^{{}},\cdots \right\}$, whose $n$th term is $\left({{a}_{n+1}}-{{a}_{n}}\right)$. Suppose that all terms in the sequence $\Delta \left( \Delta A \right)$ are $1$, and ${{a}_{18}}={{a}_{2017}}=0$, then ${{a}_{2018}}=$_______

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