
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
In the sequence $\{a\_n\}$, let $a\_i=2^{m}$ ($i∈N^{*}$, $3m-2≤slant i < 3m+1$, $m∈N^{*}$), and $S\_i=a\_i+a_{i+3}+a_{i+6}+a_{i+9}+a_{i+12}$. Find the value of $i$ that satisfies $S\_i∈[1000,3000]$.

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