
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 ratio of $8^\text{th}$ graders to $6^\text{th}$ graders in a debate club is $7:4$, and the ratio of $8^\text{th}$ graders to $7^\text{th}$ graders is $6:5$. Additionally, the ratio of $8^\text{th}$ graders to $9^\text{th}$ graders is $9:2$. What is the smallest number of students altogether in the debate club?
**A)** 256
**B)** 289
**C)** 315
**D)** 331
**E)** 348

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