
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
There are $25$ students in an extracurricular program that offers coding, chess, and photography classes. Each student must take at least one of these classes, and some may take two or even all three. The counts of students are as follows: $12$ in coding, $15$ in chess, and $10$ in photography. It is also given that there are $10$ students taking at least two classes. How many students are taking all three classes?
- **A** $2$
- **B** $3$
- **C** $1$
- **D** $4$
- **E** $5$

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