
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
Zan has modified the iterative rule for generating sequences:

1) If a number is even, increase it by 10.
2) If a number is odd, subtract 5 from it.
3) Stop when a number becomes negative.

Let $F$ be the first number in a sequence generated by the new rule. Determine if $F$ is an "even number" if -1 is not a term in the sequence that starts with $F$. How many of the whole numbers 1 through 25 are "even numbers"?

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