
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 the triangle ABC, point X lies on side AB such that CX bisects angle ACB. The lengths of segments BC, CX, and AC are given as 35, 30, and 27 respectively. Find the length of segment AX.

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