
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 $\triangle ABC$, it is known that $\tan A= \frac{1}{3}$ and $B= \frac{π}{4}$. If the ellipse $E$: $\frac{{x}^{2}}{{a}^{2}}+ \frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$ has $AB$ as its major axis and passes through point $C$, what is the eccentricity of the ellipse $E$?

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