
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
The number of intersection points between the line $\left\{\begin{aligned} x &= 2 + t \\ y &= 4 - t \end{aligned}\right.$ ($t$ is a parameter) and the curve $\left\{\begin{aligned} x &= 3 + \sqrt{2}\cos \theta \\ y &= 5 + \sqrt{2}\sin \theta \end{aligned}\right.$ ($\theta$ is a parameter) is ______.

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