
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
Given the real numbers \( a_{1}, a_{2}, \cdots, a_{18} \) that satisfy the conditions:
\[ a_{1} = 0, \left|a_{k+1} - a_{k}\right| = 1 \text{ for } k = 1, 2, \cdots, 17, \]

find the probability that \( a_{18} = 13 \).

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