
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
Three planets orbit a star circularly in the same plane.  Each moves in the same direction and moves at [constant](https://artofproblemsolving.com/wiki/index.php/Constant) speed.  Their periods are 60, 84, and 140 years.  The three planets and the star are currently [collinear](https://artofproblemsolving.com/wiki/index.php/Collinear).  What is the fewest number of years from now that they will all be collinear again?

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