
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 that in a right-angled triangle $ABC$, the right-angle side $AB$ is within plane $\alpha$, and the vertex $C$ is outside of plane $\alpha$, with the projection of $C$ onto $\alpha$ being $C_1$ (where $C_1$ is not on $AB), determine the nature of triangle $ABC_1$.

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