
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
a) Verify that \((1 + \tan k)\left(1 + \tan\left(45^{\circ} - k\right)\right) = 2\).

b) Given that

\[ 
\left(1 + \tan 1^{\circ}\right)\left(1 + \tan 2^{\circ}\right) \cdots \left(1 + \tan 45^{\circ}\right) = 2^{n} 
\]

find \( n \).

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