
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
The parabola with the equation \( y = 25 - x^2 \) intersects the \( x \)-axis at points \( A \) and \( B \).

(a) Determine the length of \( AB \).

(b) Rectangle \( ABCD \) is formed such that \( C \) and \( D \) are below the \( x \)-axis and \( BD = 26 \). Determine the length of \( BC \).

(c) If \( CD \) is extended in both directions, it meets the parabola at points \( E \) and \( F \). Determine the length of \( EF \).

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