
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
In the sequence ${{a_n}}$, ${a_1=1}$, and when ${n\geqslant 2}$, the sum of its first $n$ terms ${S_n}$ satisfies ${S_n}^2={a_n}\cdot \left( {S_n}-\frac{1}{2} \right)$. Find the expression for ${a_n}$.

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