
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
Given the sequence ${a_n}$ where all terms are integers, $a_2=4$, and for any $n∈N^{*}$, it satisfies $a_{n+1}-a_{n} < 2^{n}+ \frac{1}{2}$ and $a_{n+2}-a_{n} > 3×2^{n}-1$. Find $a_{2018}$.

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