
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 $A=\{1, 3, x^2\}$, $B=\{1, 2-x\}$, and $B \subseteq A$.
(1) Find the value of the real number $x$;  
(2) If $B \cup C = A$ and the set $C$ contains two elements, find the set C.

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