
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 that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ in $\triangle ABC$, respectively. If the area of $\triangle ABC$, $S_{\triangle ABC} = \frac{\sqrt{3}}{2}$, and $c=2$, $A=60^{\circ}$, find the values of $a$ and $b$.

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