
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
Given that $f(x) = A\sin\left(\begin{matrix} x+\frac{π}{4} \end{matrix}\right)$ where $(A\neq 0)$.

(1) If $A=1$, the vertical coordinates of each point on the graph of $f(x)$ remain unchanged, while the horizontal coordinates are expanded to twice the original. Then, the horizontal coordinates of each point on the resulting graph remain unchanged, while the vertical coordinates are expanded to twice the original, yielding the graph of $g(x)$. Find the analytical expression of $g(x)$ and the equation of its symmetry axis.

(2) If $\alpha \in [0,π]$, $f(\alpha) = \cos 2\alpha$ and $\sin 2\alpha = -\frac{7}{9}$, find the value of $A$.

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