
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]


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At Mountain Valley School, the ratio of $9^\text{th}$-graders to $7^\text{th}$-graders is $7:4$, and the ratio of $9^\text{th}$-graders to $8^\text{th}$-graders is $9:5$. Determine the smallest number of students that could be participating in this project.

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