
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 the line $\left\{\begin{array}{l}x=t \cos \alpha \\ y=t \sin \alpha\end{array}\right.$ (where $t$ is a parameter) and the circle $\left\{\begin{array}{l}x=4+2 \cos \theta \\ y=2 \sin \theta\end{array}\right.$ (where $\theta$ is a parameter) touch each other, calculate the angle of inclination of the line.

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