
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 inequality $81 \times 3^{2x} > \left( \frac {1}{9} \right)^{x+2}$.
(2) Determine the range of the function $y=3\cos\left(2x+ \frac{\pi}{4}\right)$ for $x$ in the interval $\left[0, \frac{\pi}{2}\right]$.

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