
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
In triangle \( \triangle ABC \), the interior angles \( A, B, C \) are opposite sides \( a, b, c \) respectively. Given that \( \sin^2 A + \sin^2 B - \sin^2 C = \sqrt{2} \sin A \sin B \):

1. Find angle \( C \);
2. If \( \cos B = \frac{3}{5} \), point \( D \) is on side \( BC \) such that \( CD = 4 BD \). If the area of \( \triangle ACD \) is \( \frac{7}{5} \), find \( AC \).

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