
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
The squadron of  $10$  powerful destroyers and  $20$  small boats is about to attack the island. All ships are positioned on the straight line, and are equally spaced. 

Two torpedo boats with  $10$  torpedoes each want to protect the island. However, the first torpedo boat can shoot only  $10$  successive boats, whereas the second one can shoot  $10$  targets which are next by one. Note that they have to shoot at the same moment, so that some targets may be hit by both torpedoes.

What is the biggest number of destroyers that can avoid the torpedoes no matter which targets the torpedo boats choose?

*Proposed by Bohdan Rublyov*

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