
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 set of 10 distinct integers  $S$  is chosen. Let  $M$  be the number of nonempty subsets of  $S$  whose elements have an even sum. What is the minimum possible value of  $M$ ?
<details><summary>Clarifications</summary>

- $S$  is the ``set of 10 distinct integers'' from the first sentence.
</details>

*Ray Li*

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