
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 lines intersect the $y$-axis at different points. The first line, with a $y$-intercept of 2, has a slope of 5 and an $x$-intercept $(u, 0)$. The second line, with a $y$-intercept of 3, has a slope of -7 and an $x$-intercept $(v, 0)$. What is the ratio of $u$ to $v$? Express your answer as a simplified fraction.

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