
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 fired with an initial velocity of $v$ at an angle of $\theta$ from the ground. The trajectory can be modeled by the parametric equations:
\[
x = vt \cos \theta,
\]
\[
y = vt \sin \theta - \frac{1}{2} gt^2,
\]
where \( t \) denotes time and \( g \) denotes the acceleration due to gravity. Consider $\theta$ vary over $0^\circ \le \theta \le 90^\circ.$ Find the angle $\theta$ at which the projectile just clears an obstacle located at \((\frac{v^2}{4g}, \frac{3v^2}{8g})\) before reaching its highest point.

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