
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 triangle $ABC$, with the sides opposite to angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively, and satisfying the following three conditions:

1. $a^2 + b^2 = c^2 + ab$
2. $\sqrt{3}c = 14\sin C$
3. $a + b = 13$

(1) Find the magnitude of angle $C$ and the length of side $c$.

(2) Find the area of $\triangle ABC$.

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