
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
Among nine beauties, some are always honest and tell the truth (angels), while the rest always lie (devils). The first beauty says: "There is exactly 1 devil among us"; the second beauty says: "There are exactly 2 angels among us"; the third beauty says: "There are exactly 3 devils among us"; the fourth beauty says: "There are exactly 4 angels among us"; the fifth beauty says: "There are exactly 5 devils among us"; the sixth beauty says: "There are exactly 6 angels among us"; the seventh beauty says: "There are exactly 7 devils among us"; the eighth beauty says: "There are exactly 8 angels among us"; the ninth beauty says: "There are exactly 9 devils among us." How many angels are there among these beauties?

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