
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 the ellipse \( C: \frac{x^{2}}{9} + \frac{y^{2}}{8} = 1 \) with left and right foci \( F_{1} \) and \( F_{2} \), and left and right vertices \( A \) and \( B \), respectively, a line \( l: x = my + 1 \) passing through the right focus \( F_{2} \) intersects the ellipse \( C \) at points \( M(x_{1}, y_{1}) \) and \( N(x_{2}, y_{2}) \) where \( y_{1} > 0 \) and \( y_{2} < 0 \). If \( MA \perp NF_{1} \), find the real number \( m \).

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