
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
Find the maximum value of $x+y$ for points $(x, y)$ on the ellipse given by the equation $x^2 + 3xy + 2y^2 - 14x - 21y + 49 = 0$.
A) $\frac{343}{87}$
B) $\frac{343}{88}$
C) $\frac{343}{89}$
D) $\frac{343}{90}$

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