
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
A choir forms an arrangement where there are \( x \) singers in each of \( r \) rows, with a total of less than 150 singers. There are originally three members left over when trying to form a perfect rectangular grid. If the choir director rearranges the setup by adding two more singers to each row and reducing the number of rows by 3, the new setup perfectly accommodates every member. What is the largest number of choir members possible under these conditions?

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