
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
Xiao Dong is holding a long bamboo pole and trying to enter a city gate that is $3$ meters wide. He first tries to enter horizontally but fails, then he tries to enter vertically and finds that the pole is $1$ meter taller than the gate. When he tries to enter diagonally, the ends of the pole just touch the opposite corners of the gate. What is the length of the pole in meters?

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