
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
Write down the sequence $a_1=1, a_2, a_3, \ldots, a_n$ ($n \in \mathbb{N}^*$) according to the following rule: if $a_n - 2$ is a natural number that has not been written before, then let $a_{n+1} = a_n - 2$; otherwise, let $a_{n+1} = a_n + 3$. Find the value of $a_6$.

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