
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 that the focus $F$ of the parabola $C\_1$: $y=ax^{2}(a > 0)$ is also a focus of the ellipse $C\_2$: $\frac{y^{2}}{4}+\frac{x^{2}}{b^{2}}=1 (b > 0)$, and the point $M$, $P(\frac{3}{2}, 1)$ are points on the curves $C\_1$ and $C\_2$ respectively. Find the minimum value of $(|MP|+|MF|)$.

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