
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 $a\_1=1$, $a\_2$, $a\_3$, ..., $a\_n$ ($n∈N^∗$), the rule to write the sequence is as follows: if $a\_n-2$ is a natural number and has not been written, then write $a_{n+1}=a\_n-2$; otherwise, write $a_{n+1}=a\_n+3$. Find $a\_6=$ \_\_\_\_\_\_. (Note: $0$ is a natural number)

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