
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. In triangle \( ABC \), if \( b = 2 \), \( \angle B = 30^\circ \), \( \angle C = 135^\circ \), then \( a \) equals \_\_\_\_\_\_.
2. In triangle \( ABC \), if the area of triangle \( ABC \), denoted as \( S_{\triangle ABC} \), is equal to \( \frac{1}{4} (a^2 + b^2 - c^2) \), then \( \angle C \) equals \_\_\_\_\_\_.

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