
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
(1) Solve the equation $4^x - 2^x - 2 = 0$.  
(2) Solve the inequality $\log_2(2x+3) > \log_2(5x-6)$.  
(3) Find the range of the function $y = \left(\frac{1}{3}\right)^{x^2-4x}$, where $x \in [0, 5)$.

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