
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
A non-empty finite set is called a trivial set if the sum of the squares of all its elements is an odd number. Given the set \( A = \{1, 2, 3, \ldots, 2016, 2017\} \), find the number of trivial subsets of \( A \) that are proper subsets (i.e., not equal to \( A \) itself). (You may express the answer using exponents.)

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