
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 encountered an astonishing meteor stream. Some meteors fly along a straight line at the same speed, equally spaced from each other. Another group of meteors flies in the exact same manner along another straight line, parallel to the first, but in the opposite direction, also equally spaced. The ship flies parallel to these lines. Astronaut Gavril observed that every 7 seconds the ship meets meteors flying towards it, and every 13 seconds it meets meteors flying in the same direction as the ship. Gavril wondered how often the meteors would pass by if the ship were stationary. He thought that he should take the arithmetic mean of the two given times. Is Gavril correct? If yes, write down this arithmetic mean as the answer. If not, specify the correct time in seconds, rounded to the nearest tenth.

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