
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\\), the sides opposite of the internal angles \\(A\\), \\(B\\), and \\(C\\) are respectively \\(a\\), \\(b\\), and \\(c\\). Given that \\( \\dfrac {b}{a+c}=1- \\dfrac {\\sin C}{\\sin A+\\sin B}\\) and \\(b=5\\) and \\( \\overrightarrow{AC} \cdot \\overrightarrow{AB}=5\\), find the area of \\(\\triangle ABC\\).

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