
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
In a Cartesian coordinate system, the left and right foci of the ellipse C<sub>1</sub>: $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 (a > b > 0)$$ are denoted as F<sub>1</sub> and F<sub>2</sub> respectively, where F<sub>2</sub> is also the focus of the parabola C<sub>2</sub>: $y^2 = 4x$. Point P is the intersection of C<sub>1</sub> and C<sub>2</sub> in the first quadrant, and $$|PF_{2}| = \frac{5}{3}$$.  
(Ⅰ) Find the equation of the ellipse;  
(Ⅱ) A line passing through F<sub>2</sub> and not perpendicular to the coordinate axes intersects the ellipse at points M and N. If there exists a fixed point T (t, 0) on the line segment OF<sub>2</sub> such that the quadrilateral with sides TM and TN as adjacent sides is a rhombus, determine the range of the value of t.

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