
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 that the shadow length $l$ is equal to the product of the table height $h$ and the tangent value of the solar zenith angle $\theta$, that is, $l=h\tan\theta$, and $\tan(\alpha-\beta) = \frac{1}{3}$ for the first and second solar zenith angles $\alpha$ and $\beta$, respectively, determine the ratio of the first "shadow length" to the "table height" when the "shadow length" is equal to the "table height" in the second measurement.

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