
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 a point $P(x,y)$, a line passing through it intersects the $x$-axis and $y$-axis at points $A$ and $B$, respectively. Point $Q$ is symmetric to point $P$ about the $y$-axis, and $O$ is the coordinate origin. If $\overrightarrow{BP}=3\overrightarrow{PA}$ and $\overrightarrow{OQ}\cdot\overrightarrow{AB}=4$,

1. Find the equation of the locus $M$ of point $P$.
2. A line passing through $F(2,0)$ intersects the locus $M$ at points $C$ and $D$. Find the range of values for $\overrightarrow{FC}\cdot\overrightarrow{FD}$.

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