
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]


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A cross-section in the shape of an isosceles triangle is made through vertex \( A \) of a regular tetrahedron \( ABCD \). The angle between this cross-section and the base \( BCD \) is \( 75^\circ \). How many such cross-sections can be made?

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