
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 that the graphs of $y=H(x)$ and $y=J(x)$ intersect at the points $(1, 1)$, $(3, 5)$, $(5, 10)$, and $(7, 10)$. Determine one point where the graphs of $y=H(3x)$ and $y=3J(x)$ must intersect. What is the sum of the coordinates of that point?

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