
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
What is the distance $x$ at which the shot put reaches the ground, i.e. where $y=0$, given that the relationship between the height $y$ and the horizontal distance $x$ is given by $y=-\frac{1}{12}x^{2}+\frac{2}{3}x+\frac{5}{3}$?

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