
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 $a\_1=\frac{1}{2}$, $a\_2=\frac{1}{3}(1-a\_1)=\frac{1}{6}$, $a\_3=\frac{1}{4}(1-a\_1-a\_2)=\frac{1}{12}$, $a\_4=\frac{1}{5}(1-a\_1-a\_2-a\_3)=\frac{1}{20}$, and so on. Find the general term $a\_n$ when $n \in \mathbb{N}^*$.

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