
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
Three rods (with negligible thickness) are fixed perpendicularly to each other at a common point at one end. The lengths of the rods are 1, 2, and 3. This construction is placed on a table in such a way that the free ends of the rods lie on the plane of the tabletop. Determine the exact height of the fixed point above the table.

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