
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 lines $C\_1$ and $C\_2$ with parameterized equations:
$C\_1$: $\begin{cases} x = 1 + t \cos \alpha \\ y = t \sin \alpha \end{cases} (t \text{ is the parameter})$,
$C\_2$: $\begin{cases} x = \cos \theta \\ y = \sin \theta \end{cases} (\theta \text{ is the parameter})$.
Find the coordinates of the intersection point(s) when $\alpha = \frac{\pi}{3}$.

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