
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 the quadratic function \( y = ax^2 + bx + c \) where \( a \neq 0 \), its vertex is \( C \), and it intersects the x-axis at points \( A \) and \( B \). If triangle \( \triangle ABC \) is an acute triangle and \(\sin \angle BCA = \frac{4}{5}\), find the discriminant \(\Delta = b^2 - 4ac\).

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