
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

Set
$$
\left\{(a, b, c, d, e) \left\lvert\, \log _{\frac{1}{6}}\left(a^{6}+b^{6}+c^{6}+d^{6}+e^{6}+1\right) \geq \log _{\frac{1}{6}} a+\log _{\frac{1}{6}} b+\log _{\frac{1}{6}} c+\log _{\frac{1}{6}} d+\log _{\frac{1}{6}} e-1\right.\right\}
$$

has a subset.

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