
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
A yacht sails \( 15 \) miles in a straight line from \( A \) to \( B \), then turns through an angle between \( 30^{\circ} \) and \( 75^{\circ} \), and sails another \( 25 \) miles to \( C \). Calculate the range of possible values for \( AC^2 \).

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