
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
There are hidden reefs around a small island, which are distributed within a circular area with a radius of $20$ km centered on the island. It is known that the center of the island is located $10a$ km west (where $a > 0$) of the ship, and the port is located $40$ km north of the center of the island. If the ship returns to the port along a straight line without the danger of running aground, find the range of values for $a$.

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