
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 set $\mathcal{C}$ be a 50-element subset of even numbers from the set $\{2,4,6,...,200\}$. What is the sum $P$ of the elements of $\mathcal{C}$ and how many possible values can $P$ take?

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