
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. Due to the presence of wind, the projectile's trajectory is affected by a horizontal wind velocity $w_h$ and a vertical wind velocity $w_v$. The modified parametric equations for the projectile's trajectory are:
\[
x = (vt + w_h t) \cos \theta,
\]
\[
y = (vt + w_v t) \sin \theta - \frac{1}{2} gt^2,
\]
where $t$ denotes time, $g$ denotes acceleration due to gravity, $w_h$ and $w_v$ are the constant horizontal and vertical wind velocities respectively.

Assuming $v = 100$ m/s, $w_h = 10$ m/s, $w_v = -2$ m/s, $\theta = 45^\circ$, and $g = 9.8$ m/s², find the highest point $(x, y)$ reached by the projectile.

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