
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 triangle $ABC$, if there exists triangle $A_1B_1C_1$ such that $$\frac{\cos A}{\sin A_1} = \frac{\cos B}{\sin B_1} = \frac{\cos C}{\sin C_1} = 1,$$ then triangle $A_1B_1C_1$ is called the "dual" triangle of triangle $ABC$. If an isosceles triangle $ABC$ has a "dual" triangle, then the radian measure of its base angle is ___________.

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