
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 transgalactic ship encounters an astonishing meteor shower. Some of the meteors are flying along a straight line with the same speeds, one after another, and equidistant from each other. Another group of meteors flies similarly along another straight line, parallel to the first, but in the opposite direction, also equidistant from each other. The ship is flying parallel to these lines. Astronaut Gavrila observed that every 7 seconds the ship meets meteors flying towards it, and every 13 seconds it meets meteors going in the same direction as the ship. He wondered how frequently the meteors would pass by if the ship were stationary. He thought that he needed to take the arithmetic mean of the two given times. Is Gavrila correct? If yes, then provide this arithmetic mean as the answer. If no, specify the correct time in seconds, rounded to the nearest tenth.

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