
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 regular triangular pyramid has its side face forming an angle $\varphi$ with the base. The angle between any two adjacent lateral edges is denoted by $\varepsilon$. Express $\varepsilon$ as a function of $\varphi$.

a) For what value of $\varphi$ is $\varepsilon=45^{\circ}$?  
b) For what value of $\varepsilon$ is $\varphi=45^{\circ}$?

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