
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
Given that $\overrightarrow{e_1}$ and $\overrightarrow{e_2}$ are unit vectors and the non-zero vector $\overrightarrow{a}=x\overrightarrow{e_1}+y\overrightarrow{e_2}$, where $x$, $y\in \mathbb{R}$, find the maximum value of $\frac{|y|}{|\overrightarrow{a}|}$.

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