
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]


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The cardinality of a finite set \\(P\\) is denoted as \\(\text{card}(P)\\). It is known that \\(\text{card}(M) = 10\\), \\(A \subseteq M\\), \\(B \subseteq M\\), \\(A \cap B = \varnothing\\), and \\(\text{card}(A) = 2\\), \\(\text{card}(B) = 3\\).

\\((1)\\) If set \\(X\\) satisfies \\(A \subseteq X \subseteq M\\), find the number of such sets \\(X\\).

\\((2)\\) If set \\(Y\\) satisfies \\(Y \subseteq M\\), \\(A \not\subset Y\\), \\(B \not\subset Y\\), find the number of such sets \\(Y\\).

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