
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 matrix $A= \begin{pmatrix} a & 2 \\ -1 & 4 \end{pmatrix}$. A has an eigenvalue $\lambda=2$.
(1) Determine matrix $A$;
(2) In the Cartesian coordinate system, point $P(1, 1)$ is successively transformed by the transformation $\sigma$ corresponding to matrix $A$ and the reflection transformation $\gamma$ with respect to the x-axis to obtain point $P'$. Write the formula for the composite transformation $\gamma \circ \sigma$ and find the coordinates of point $P'$.

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