
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
Let \( A = \{1, 2, 3, 4, \ldots, 1000\} \). Let \( m \) be the number of 2-element subsets \(\{a, b\}\) of \( A \) such that \( a \times b \) is divisible by 6. Find the value of \(\lfloor m / 10 \rfloor\). (Here and in subsequent questions \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \).)

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