
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
If $\alpha$ and $\beta$ are acute angles, and $\alpha + \beta = \frac{\pi}{4}$, then $\left(1+\tan \alpha \right)\left(1+\tan \beta \right)=$____; $\left(1+\tan 1^{\circ}\right)\left(1+\tan 2^{\circ}\right)\left(1+\tan 3^{\circ}\right)\cdots \left(1+\tan 45^{\circ}\right)=$____.

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