
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 $l = h \tan \theta$, for two measurements with the same "table height" $h$, if $\tan(\alpha-\beta) = \frac{1}{3}$ and the second "shadow length" $l_2$ equals the "table height" $h$, calculate the first "shadow length" $l_1$ in terms of $h$.

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