
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 ball is thrown from the surface of the Earth at an angle of $45^{\circ}$ with a speed of $v_{0}=20 \text{ m/s}$. How long will it take for the velocity vector of the ball to turn by $90^{\circ}$? Neglect air resistance. The acceleration due to gravity is $g=10 \text{ m/s}^2$.

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