
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 ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$, point $P(1,1)$ is inside the ellipse, $F\_1$ is the left focus of the ellipse, and $M$ is a moving point on the ellipse:

(Reasoning) Find the minimum value of $|MP| + \frac{3}{2}|MF\_1|$;

(Textual) Find the range of values for $|MP| + |MF\_1|$.

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