
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
In the rectangular coordinate system $(xOy)$, point $M(-2,0)$. Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of the $x$-axis as the polar axis. Point $A(ρ,θ)$ is on curve $C$, and point $B(ρ,θ+\frac{π}{3})$ satisfies $|BM|=1$.

(1) Find the rectangular coordinate equation of curve $C$.
(2) Find the range of values for $|OA|^2+|MA|^2$.

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