
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 $A = \{x \mid x^2 - 3x + 2 = 0\}$, $B = \{x \mid x^2 - ax + 2 = 0\}$, with the condition that $B \subseteq A$.
1. List all subsets of set $A$.
2. If set $B$ is non-empty, find the value of $a$.

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