
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
Given sets $A = \{x | x^2 - 3x + 2 = 0, x \in \mathbb{R}\}$ and $B = \{x | 0 < x < 5, x \in \mathbb{N}\}$, find the number of sets $C$ such that $A \subseteq C \subseteq B$.

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