
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 is a clock on the town hall tower that has a small door near the center of the dial used during maintenance. However, the door opens outward, which is impractical — for example, exactly at 12:09, the minute hand covers the door, and it cannot be opened until exactly 12:21.

How many minutes per day is the door not able to be opened?

(Remember that the door can also be covered by the hour hand; the entire door lies within the circle described by this hand.)

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