
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 projectile is launched upward with an initial velocity $v_0$ meters per second from a height $h_0$ meters above the ground. Assuming acceleration due to gravity is $10 \, \text{m/s}^2$, for what value of $v_0$ will the maximum height reached by the projectile be exactly 45 meters above its initial launch height?

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