
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
Two triangles $ABC$ and $DEF$ are given. $AB = 6$ units, $BC = 11$ units, $AC = x$ units, and $DE = 6$ units, $EF = 9$ units, $DF = 10$ units. If $\angle ABC = \angle DEF$, find the length of $AC$.

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