
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 $x, y \in \mathbb{N}$, find the maximum value of $y$ such that there exists a unique value of $x$ satisfying the following inequality:
$$
\frac{9}{17}<\frac{x}{x+y}<\frac{8}{15}.
$$

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