
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
In right-angled triangle $ABC$, the hypotenuse lies on plane $\alpha$, and the right-angle vertex $C$ is a point outside plane $\alpha$. The angles formed by $AC$ and $BC$ with plane $\alpha$ are $30^\circ$ and $45^\circ$, respectively. Then, the acute angle formed by plane $ABC$ and $\alpha$ is

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