
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
Two partners, Smag and Williamson, have decided to take on a third partner, Mr. Rogers. Smag invested $1 \(\frac{1}{2}\) times more capital than Williamson. Rogers is to invest $2500, which should be divided between the other two partners so that the shares of all three partners become equal afterwards. How should the amount invested by Rogers be divided?

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