
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 a curve with the parametric equations
\[
\begin{cases} 
x=3\cos \theta, \\
y=4\sin \theta 
\end{cases}
\]
where $\theta$ is the parameter, $(0\leqslant \theta\leqslant \pi)$, and a point $P$ on the curve such that the line $OP$ (from $P$ to the origin $O$) has an inclination angle of $\dfrac{\pi}{4}$, find the coordinates of point $P$.

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