
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 the set \( X = \{1, 2, \cdots, n\} \). A non-empty subset \( A \) of \( X \) is called an "odd subset" if the number of odd elements in \( A \) is greater than the number of even elements. Find:
(1) The number of odd subsets of \( X \);
(2) The total sum of the elements of all odd subsets of \( X \).

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