
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 pizza is cut into 10 pieces. Two of the pieces are each $\frac{1}{24}$ of the whole pizza, four are each $\frac{1}{12}$, two are each $\frac{1}{8}$, and two are each $\frac{1}{6}$. Determine the sum of the values of $n$ with $2 \leq n \leq 10$ for which it is not possible to distribute all of these pieces equally among $n$ friends.

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