
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

Solve the inequality $\log _{1+x^{2}}\left(1-27 x^{5}\right)+\log _{1-3 x^{2}+36 x^{4}}\left(1+x^{2}\right) \leqslant 1+\log _{1-3 x^{2}+36 x^{4}}\left(1-27 x^{5}\right)$. 

Answer: $x \in\left\{-\frac{1}{3}\right\} \bigcup\left(-\frac{1}{2 \sqrt{3}} ; 0\right) \cup\left(0 ; \frac{1}{2 \sqrt{3}}\right) \cup\left[\frac{1}{3} ; \frac{1}{\sqrt[5]{27}}\right)$.

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