
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 $\left\{a_{n}\right\}$:
$$
a_{0}=1, \quad a_{n}=2 \sum_{i=0}^{n-1} a_{i} \quad (n \geqslant 1).
$$

Find the largest positive integer $n$ such that $a_{n} \leqslant 2018$.

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