
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 construction rule of the sequence $\{a_{n}\}$ is as follows: $a_{1}=1$, if $a_{n}-2$ is a natural number and has not appeared before, then use the recursive formula $a_{n+1}=a_{n}-2$. Otherwise, use the recursive formula $a_{n+1}=3a_{n}$, then $a_{6}=$ _____.

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