
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 \( \triangle ABC \), point \( D \) is on side \( BC \). Given \( AB = 13 \), \( AD = 12 \), \( AC = 15 \), and \( BD = 5 \), find \( DC \).

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