
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
For a non negative integer  $n$ , set t  $I_n=\int_0^{\frac{\pi}{4}} \tan ^ n x\ dx$  to answer the following questions:

(1) Calculate  $I_{n+2}+I_n.$ (2) Evaluate the values of  $I_1,\ I_2$  and  $I_3.$ 1978 Niigata university entrance exam

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