
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 prism \(A B C A_1 B_1 C_1\), the medians of the bases \(A B C\) and \(A_1 B_1 C_1\) intersect at points \(O\) and \(O_1\) respectively. A line is drawn through the midpoint of the segment \(O O_1\) parallel to the line \(C A_1\). Find the length of the segment of this line that lies inside the prism, given that \(C A_1 = a\).

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