
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) Find the maximum value of the function $f(x) = 4^{x- \frac {1}{2}} - 3 \cdot 2^x + 5$ in the interval [-2, 2], and find the value of $x$ when $f(x)$ reaches its maximum value.  
(2) If the maximum value of the function $y = a^{2x} + 2a^x - 1$ ($a > 0$, $a \neq 1$) in the interval [-2, 2] is 14, find the value of the real number $a$.

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