
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 $T = \{(x, y) | ax + y - 3 = 0\}$ and $S = \{(x, y) | x - y - b = 0\}$. If $S \cap T = \{(2, 1)\}$, then find the product $a \cdot b$.

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