
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 $ABC$, $AB=c$, $BC=a$, $AC=b$, and $a$, $b$, $c$ satisfy the following three equations: 
1. $a+ac+bc=2b$
2. $a-ac+bc=2c$
3. $a=b+c+2bc\cdot\cos A$

Find the largest angle in triangle $ABC$ and its measure in degrees.

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