
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 cake has a shape of triangle with sides  $19,20$  and  $21$ . It is allowed to cut it it with a line into two pieces and put them on a round plate such that pieces don't overlap each other and don't  stick out of the plate. What is the minimal diameter of the plate?

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