
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
In a class of 42 girls, three students are favorites: an actor ( $S z$ ), a fencing champion $(V)$, and a skating champion $(K)$. The girls collect autographed photos of their favorites. Six girls already have such photos from all three favorites. The class collectively has $21 S z$ photos, $20 V$ photos, and $18 K$ photos. In response to the question of who has both an $S z$ photo and a $V$ photo, 7 girls raised their hands. Similarly, 10 girls raised their hands for having $S z$ and $K$ photos, and 11 girls for having $V$ and $K$ photos. Is there any girl who does not have an autographed photo from any of her favorites, and if so, how many such girls are there?

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