
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
Harry Potter found a mysterious diary written by Voldemort in the Chamber of Secrets, which documented a special operator $\oplus$. Fortunately, Harry discovered a clue on the title page: $A \oplus B = \frac{1}{A \times B} + \frac{1}{(A+1) \times (B+\square)}$. It is known that $1 \oplus 2 = \frac{5}{8}$, but unfortunately, the number inside the “ $\square$ ” is unclear. Harry must calculate the result of $9 \oplus 10$ to destroy Voldemort's diary, so what is $9 \oplus 10 =\ $? (Express the result as a simplified fraction.)

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