
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
Given 500 members voting, a city council initially defeated a proposal. In a subsequent vote, with the same members participating, the proposal was passed by one and a half times the margin by which it was originally defeated. The number voting for the proposal in the re-vote was $\frac{13}{12}$ of the number voting against it originally. Determine how many more members voted for the proposal in the re-vote compared to the initial vote.

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