
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
Find the coordinates of the intersection point(s) between the line defined by the parametric equations $x = 1 - \frac{\sqrt{5}}{5}t$, $y = -1 + \frac{2\sqrt{5}}{5}t$ (where $t$ is the parameter) and the curve defined by the parametric equations $x = \sin\theta \cdot \cos\theta$, $y = \sin\theta + \cos\theta$ (where $\theta$ is the parameter).

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