
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 $A \times B = \{(a, b) | a \in A, b \in B\}$. For example, if $A = \{1, 2\}$ and $B = \{3, 4\}$, then $A \times B = \{(1, 3), (1, 4), (2, 3), (2, 4)\}$. Now, given $A \times B = \{(1, 1), (2, 1), (3, 1)\}$, find the number of subsets of $A$.

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