
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 lengths of sides opposite to angles A, B, C are denoted by a, b, c respectively. If \( c = \sqrt{3} \), \( b = 1 \), and \( B = 30^\circ \),
(1) find angles A and C;
(2) find the area of \( \triangle ABC \).

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