
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
Read from the equations

$$
\begin{aligned}
& x^{2}+y^{2}=r^{2} \\
& b^{2} x^{2}+a^{2} y^{2}=b^{2} a^{2} \\
& b^{2} x^{2}-a^{2} y^{2}=b^{2} a^{2} \\
& y^{2}=2 p x \\
& y=\sin x \\
& y=\operatorname{tang} x \\
& y=\log x
\end{aligned}
$$

the symmetrical properties of the curves they represent.

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