
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 a sequence $\{a\_n\}$ that satisfies: $a\_1=1$, $a\_{2n}=a\_{2n-1}+1$, $a\_{2n+1}=2a\_{2n}+1$, $n\in\mathbb{N}^*$, let $S\_n$ be the sum of the first $n$ terms of the sequence. Find the minimum value of the positive integer $k$ such that $S\_k > 2018$.

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