
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 $A=\{x|x=2^{\alpha}\cdot3^{\beta}, \alpha, \beta \in \mathbb{Z} \text{ and } \alpha \geq 0, \beta \geq 0\}$, and $B=\{x|1 \leq x \leq 5\}$. Find the set of real numbers $A \cap B$.

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