Two hanging masses share an acceleration

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Problem: Two hanging masses share an acceleration
Masses 3 kg and 2 kg hang from opposite ends of a string over an ideal pulley. They are released.
Question: Find the acceleration magnitude.
Givens:
- m₁ = 3 kg
- m₂ = 2 kg
Assumptions: g = 10 m/s²; massless inextensible string, frictionless massless pulley and no air resistance.
Choices (LaTeX):
A. 0\ \mathrm{m\,s^{-2}}
B. 2\ \mathrm{m\,s^{-2}}
C. 10\ \mathrm{m\,s^{-2}}
D. 5\ \mathrm{m\,s^{-2}}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.