
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
The height of the taller tree is unknown. Let the height of the taller tree be $x$ feet. Since the other tree is $20$ feet shorter, the height of the shorter tree is $x-20$ feet. The two heights are in the ratio $5:7$, so we can set up the equation $\frac{x}{x-20}=\frac{5}{7}.$ Solve for $x$ to find the height of the taller tree.

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