
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
Let $x$ be the larger of the two positive numbers, and let $y$ be the smaller of the two positive numbers. The sum of the two numbers is $x+y$, and their difference is $x-y$. The sum of the two numbers is $7$ times their difference, so we have the equation $x+y=7(x-y)$. Solve this equation for the ratio of $x$ to $y$.

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