
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
a) An electrical circuit has the structure of a $3 \times 3$ grid: the circuit has a total of 16 nodes (the vertices of the squares in the grid) which are connected by wires (the sides of the squares in the grid). Some of the wires may have burned out. With one measurement, you can select any pair of nodes in the circuit and check whether a current flows between them (i.e., check whether there is a chain of unburnt wires connecting these nodes). In fact, the circuit is such that a current flows from each node to any other. What is the minimum number of measurements needed to always verify this?

b) Answer the same question for a $5 \times 5$ grid (a total of 36 nodes).

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