
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
Given the curve defined by the parametric equations $\begin{cases}x=3\cos \theta \\\ y=4\sin \theta\end{cases}$ where $\theta$ is a parameter, $0\leqslant \theta\leqslant \pi$, the slope angle of the line $PO$ passing through a point $P$ on the curve and the origin $O$ is $\frac{\pi}{4}$. Determine the coordinates of point $P$.

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