
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 $\{a\_n\}$ that satisfies $a\_1=1$, $a_{n+1}= \begin{cases} a\_n+1,a\_n < 3 \\\\ \frac {a\_n}{3},a\_n\geqslant 3\end{cases}$, find the sum of the first 12 terms of the sequence, denoted as $S_{12}=$ ___.

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