
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 $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1 (a > b > 0)$ with two focal points $F\_1(-1,0)$ and $F\_2(1,0)$. The ellipse passes through the point $P(\frac{4}{3}, \frac{1}{3})$. Find the equation of ellipse $C$.

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