
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
A point whose x-coordinate and y-coordinate are both integers is called an integer point. Let $a$ and $b$ be positive numbers greater than $1$, and $ab+a-b-10=0$. If the minimum value of $a+b$ is $m$, then the number of integer points $(x,y)$ that satisfy $3x^{2}+2y^{2} \leqslant m$ is \_\_\_\_\_\_.

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