
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
Four statements were made about triangle \(ABC\), and we know that out of these statements, two are true and two are false. What could be the perimeter of triangle \(ABC\) if \(BC = 1\)?

I. Triangle \(ABC\) is a right triangle.
II. The angle at \(A\) is \(30^\circ\).
III. \(AB = 2 \times BC\).
IV. \(AC = 2 \times BC\).

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