
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 \( C: \frac{x^{2}}{3}+\frac{y^{2}}{2}=1 \) and a point \( P \) on this ellipse, draw a perpendicular from \( P \) to the right directrix of the ellipse at point \( H \). Extend \( P H \) to a point \( Q \) such that \( |H Q|=\lambda|P H| \) (where \( \lambda \geqslant 1 \)). As point \( P \) moves on the ellipse \( C \), find the range of values for the eccentricity of the trajectory of point \( Q \).

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