
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
Through the right focus \( F \) of the ellipse \( C: \frac{x^2}{2} + y^2 = 1 \), draw a line \( l \) that intersects the ellipse \( C \) at two different points \( A \) and \( B \). Suppose \( \overrightarrow{FA} = \lambda \overrightarrow{FB} \) and \( T(2,0) \). If \( \lambda \in [-2, -1] \), find the range of values of \( |\overrightarrow{TA} + \overrightarrow{TB}| \).

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