
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
Consider the ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$. The upper vertex of the ellipse is $B$. Two lines, $l_{1}$ and $l_{2}$, pass through point $B$ and are perpendicular to each other. They intersect the ellipse at points $P$ and $Q$ respectively. When the slope of $l_{1}$ is $2$, the coordinates of point $P$ are $(-\frac{5}{3}, -\frac{4}{3})$.

1. Find the equation of ellipse $C$.
2. If line $PQ$ intersects the $y$-axis at point $M$, and $\overrightarrow{PM}=\lambda \overrightarrow{MQ}$, find the range of values for $\lambda$.

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