
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 \( a, b, c \) are the sides opposite to \(\angle A, \angle B, \angle C\) respectively in \(\triangle ABC\), and \( S \) is the area of \(\triangle ABC\). If \( a = 4 \), \( b = 5 \), and \( S = 5 \sqrt{3} \), find the length of \( c \).

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