
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
Find the second-order derivative \( y_{xx}^{\prime \prime} \) of the function given parametrically.

\[
\left\{\begin{array}{l}
x=\frac{\cos t}{1+2 \cos t} \\
y=\frac{\sin t}{1+2 \cos t}
\end{array}\right.
\]

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