
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 line $y=-x+m$ intersects the ellipse $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$ at points $A$ and $B$. The eccentricity of the ellipse is $\frac{\sqrt{3}}{3}$, and the focal length is $2$.
(1) Find the equation of the ellipse;
(2) If vector $\overset{→}{OA} \cdot \overset{→}{OB} =0$ (where $O$ is the origin), find the value of $m$.

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