
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
The sequence ${a_n}$ satisfies $a_1=1$, and $a_n=$ $\begin{cases} 2a_{n-1}-1,&n\text{ is even}\\ 2a_{n-1}+2,&n\text{ is odd}\end{cases}$. Calculate the minimum number of moves required to solve 4 rings.

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