
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
Laura has 2010 lights and 2010 switches, with each switch controlling a different light. She wants to determine which switch corresponds to which light. To achieve this, Charlie will operate the switches. Each time, Charlie presses some switches simultaneously, and the number of lit lights is the same as the number of switches pressed (note: after each operation, the switches return to their original state). 

Questions:
(1) What is the maximum number of different operations Charlie can perform so that Laura can accurately determine the correspondence between the switches and lights?
(2) If Laura operates the switches herself, what is the minimum number of operations needed to determine the correspondence between the switches and lights?

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