
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 following inequalities (system):
(1) $2^{x^2-3x-5} \geq \left(\frac{1}{2}\right)^{x+2}$;  
(2) $\begin{cases} \frac{2x+1}{x-3} > 1 \\ x^2+x-20 \leq 0 \end{cases}$.

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