
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 C₁: $$\frac {x^{2}}{a^{2}}$$+ $$\frac {y^{2}}{b^{2}}$$\=1 (a>b>0) with left and right foci F₁ and F₂, and an eccentricity of $$\frac { \sqrt {3}}{2}$$. The parabola C₂: y²=2px (P>0) has a focus at F₂. The chord length of the parabola C₂ intercepted by the line perpendicular to the x-axis through the midpoint Q of OF₂ is 2$$\sqrt {6}$$.

1. Find the standard equation of the ellipse C₁.
2. Let T be a moving point on the ellipse C₁ that satisfies: $$\overrightarrow {OT}$$\=$$λ \overrightarrow {OA}$$+2$$μ \overrightarrow {OB}$$, where A and B are points on the ellipse C₁, and the product of the slopes of lines OA and OB is -$$\frac {1}{4}$$. If N(λ, μ) is a moving point and P satisfies $$\overrightarrow {PQ}= \frac {1}{2} \overrightarrow {F_{1}F_{2}}$$, investigate whether |NP|+|NQ| is a constant value. If it is, find the value; if not, provide a reason.

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