
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
$$\tan (n+1)^{\circ}-\tan n^{\circ} =\frac{\sin (n+1)^{\circ}}{\cos (n+1)^{\circ}}-\frac{\sin n^{\circ}}{\cos n^{\circ}}=\frac{\sin (n+1)^{\circ} \cos n^{\circ}-\cos (n+1)^{\circ} \sin n^{\circ}}{\cos n^{\circ} \cdot \cos (n+1)^{\circ}} =\frac{\sin 1^{\circ}}{\cos n^{\circ} \cdot \cos (n+1)^{\circ}}.$$

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