use this template:
### Expanded Template for Deductive and Inductive Reasoning Using Scientific Theory

#### Deductive Reasoning Template
1. Define the Theory or Principle:
- [State the overarching scientific theory or principle that will guide the reasoning process.]
- Example: Newton's Laws of Motion

2. Formulate a Hypothesis:
- [Derive a specific hypothesis or prediction based on the theory.]
- Example: If an object is in motion, it will remain in motion unless acted upon by an external force.

3. Identify Relevant Observations or Data:
- [List the observations or data that will be used to test the hypothesis.]
- Example: Observations of a rolling ball on a flat surface.

4. Apply Logical Reasoning:
- [Use logical steps to connect the theory to the hypothesis and observations.]
- Example:
- Premise 1: According to Newton's First Law, an object in motion will remain in motion unless acted upon by an external force.
- Premise 2: The rolling ball is an object in motion.
- Conclusion: The rolling ball will continue to roll unless an external force (like friction) acts upon it.

5. Evaluate the Conclusion:
- [Assess whether the conclusion aligns with the observations and the theory.]
- Example: The rolling ball eventually stops due to friction, confirming Newton's First Law.

6. Refine the Hypothesis or Theory (if necessary):
- [Adjust the hypothesis or theory based on the evaluation.]
- Example: Include the effect of friction in the hypothesis.

7. Document the Reasoning Process:
- [Record the logical steps, observations, and conclusions for future reference.]
- Example: Write a report detailing the logical reasoning process and the results.

8. Communicate Findings:
- [Share the results with peers or the scientific community for feedback and validation.]
- Example: Present findings at a scientific conference or publish in a journal.

#### Inductive Reasoning Template
1. Gather Observations or Data:
- [Collect a series of observations or data points relevant to the scientific theory.]
- Example: Observations of various objects falling to the ground.

2. Identify Patterns or Trends:
- [Look for consistent patterns or trends in the collected data.]
- Example: All observed objects fall towards the ground when dropped.

3. Formulate a General Hypothesis:
- [Create a general hypothesis based on the identified patterns.]
- Example: All objects fall towards the ground due to gravity.

4. Test the Hypothesis:
- [Design experiments or gather additional data to test the hypothesis.]
- Example: Drop different objects from varying heights and observe their behavior.

5. Refine the Hypothesis:
- [Adjust the hypothesis based on the results of the tests.]
- Example: Include the effect of air resistance in the hypothesis.

6. Develop a Theory:
- [Formulate a broader scientific theory that explains the refined hypothesis.]
- Example: Theory of Gravity: All objects are attracted towards the Earth due to gravitational force.

7. Apply the Theory to New Observations:
- [Use the theory to predict and explain new observations.]
- Example: Predict that a feather will fall slower than a stone due to air resistance.

8. Evaluate and Refine the Theory:
- [Continuously assess the theory against new data and refine it as necessary.]
- Example: Incorporate the concept of gravitational acceleration in the theory.

9. Document the Reasoning Process:
- [Record the logical steps, observations, and conclusions for future reference.]
- Example: Write a report detailing the logical reasoning process and the results.

10. Communicate Findings:
- [Share the results with peers or the scientific community for feedback and validation.]
- Example: Present findings at a scientific conference or publish in a journal.

### Command Terms Glossary
- Define: Provide a clear and concise explanation of a concept or term.
- Formulate: Create or develop a hypothesis or theory based on available information.
- Identify: Recognize and list relevant data, patterns, or trends.
- Apply: Use a theory or principle to explain or predict phenomena.
- Evaluate: Assess the validity or reliability of a hypothesis, theory, or conclusion.
- Refine: Adjust or improve a hypothesis or theory based on new evidence.
- Test: Conduct experiments or gather data to verify a hypothesis.
- Develop: Build or expand a theory based on refined hypotheses.
- Document: Record the logical steps, observations, and conclusions for future reference.
- Communicate: Share findings with peers or the scientific community for feedback and validation.
Note: Code/Python/Calculators are not applicable in verifying answers unless the answer pertains to creating such elements.

### user query ###
What's the long diagonal of a regular hexagon with the short diagonal of 64?

Before starting your template, provide your full reasoning in latin. Or, in whichever non-english way you prefer :)