
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
The radius of the circle inscribed in triangle \(ABC\) is 4, with \(AC = BC\). On the line \(AB\), point \(D\) is chosen such that the distances from \(D\) to the lines \(AC\) and \(BC\) are 11 and 3 respectively. Find the cosine of the angle \(DBC\).

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