
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 an ellipse $E$: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with one of its foci being $F_2(1,0)$, and the ellipse passes through a fixed point $M(1, \frac{\sqrt{2}}{2})$.
(I) Find the standard equation of ellipse $E$;
(II) Let point $Q(2,0)$, draw a line $l$ passing through point $F_2$ and intersecting with ellipse $E$ at points $A$ and $B$, and $\overrightarrow{F_2A} = λ\overrightarrow{F_2B}$, where $λ ∈ [-2,-1]$. Construct a parallelogram $QACB$ with sides $QA$ and $QB$. Find the minimum length of the diagonal $QC$.

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