
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

To lift a load, it is attached to the hook of a crane using slings made of steel ropes. The calculated mass of the load is \( M = 20 \) tons, and the number of slings is \( n = 3 \). Each sling forms an angle of \( \alpha = 30^\circ \) with the vertical. All slings carry an equal load when lifting the cargo. According to safety requirements, the breaking strength of the rope must exceed the calculated load by a factor of \( k = 6 \). The rope consists of a very large number of steel threads, each of which withstands a maximum load of \( q = 10^3 \mathrm{N/mm}^2 \). Specify the smallest diameter of the rope that can be used to make the slings, given that ropes with any whole millimeter diameter are available. Assume the free fall acceleration \( g \) to be \( 10 \mathrm{m/s}^2 \).

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