
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
My friend, who is vegan and allergic to gluten and nuts, and I went to a local cafe. The cafe menu lists 30 dishes in total. 1/3 of these dishes are vegan, and 2/5 of the vegan dishes contain gluten. Additionally, 1/4 of the vegan dishes contain nuts. What fraction of the items on the menu at this cafe can my friend eat?

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