
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 nine-linked rings is a type of puzzle game that has been widely popular in our country since ancient times. In a certain way of playing, $a_n$ represents the minimum number of moves required to solve $n$ ($n\leq9$, $n\in\mathbb{N}^*$) rings. It is known that $a_1=1$, and $a_n=$ $\begin{cases} 2a_{n-1}-1, & n \text{ is even} \\ 2a_{n-1}+2, & n \text{ is odd} \end{cases}$, then the minimum number of moves required to solve 4 rings, $a_4$, is _____.

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