
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
Four crates, each containing a different item (oranges, apples, cucumbers, and potatoes), were delivered to a store. The crates are numbered from 1 to 4, and each has the following label:

- Crate 1: "The potatoes are in crate 2."
- Crate 2: "The oranges are not in this crate."
- Crate 3: "The apples are in this crate."
- Crate 4: "The cucumbers are in crate 1 or crate 2."

It turned out that the labels on the fruit crates (oranges and apples) are false, and the labels on the vegetable crates (cucumbers and potatoes) are true. Determine what is in each crate.
(a) In the first crate
(1) there are oranges
(b) In the second crate
(2) there are apples
(c) In the third crate
(3) there are cucumbers
(d) In the fourth crate
(4) there are potatoes

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