
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
What angle should the forces $p_{1}$ and $p_{2}$ form so that their resultant is equal to their arithmetic mean? What ranges should the ratios $\frac{p_{1}}{p_{2}}$ (and similarly, $\frac{p_{2}}{p_{1}}$) fall within for the problem to have a solution? What ranges should the angle between the two forces be in?

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