
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
Let there be two fixed points in a plane, $F_1(-\sqrt{5}, 0)$ and $F_2(\sqrt{5}, 0)$. The lines $PF_1$ and $PF_2$ intersect at point $P$, and the product of their slopes is a constant $-\frac{4}{5}$.  
(Ⅰ) Find the equation of the trajectory $C_1$ of the moving point $P$;  
(Ⅱ) Let $M(0, \frac{1}{5})$, and $N$ be a moving point on the parabola $C_2: y=x^2$. Draw the tangent line to the parabola $C_2$ at point $N$ that intersects curve $C_1$ at points $P$ and $Q$. Find the maximum value of the area of $\triangle MPQ$.

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