
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
Determine the addition theorem for the tangent function without using the addition theorems for sine and cosine functions, as is usually done in textbooks. (Restrict to the case where both addends and their sum are positive acute angles.)

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