
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:
\[ \log_{5} 250 + \left(4 - (\log_{5} 2)^2\right) \log_{50} 5 \leqslant 125^{(\log_{5} x)^2} - 24 \cdot x^{\log_{5} x} \]

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