
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
An easel in a corner hosts three $30 \text{ cm} \times 40 \text{ cm}$ shelves, with equal distances between neighboring shelves. Three spiders resided where the two walls and the middle shelf meet. One spider climbed diagonally up to the corner of the top shelf on one wall, another climbed diagonally down to the corner of the lower shelf on the other wall. The third spider stayed in place and observed that from its position, the other two spiders appeared at an angle of $120^\circ$. What is the distance between the shelves? (The distance between neighboring shelves is the same.)

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