Problem

In embedded systems such as firmware interacting with Meta hardware, registers are often updated by changing one bit at a time. Write a function that applies a sequence of bit operations to an integer register.

Given an initial integer register, and a list of operations ops, return the final register value after processing each operation in order. Each operation is a pair [action, bit_index], where action is one of:

• "set": set the bit at bit_index to 1
• "clear": clear the bit at bit_index to 0
• "toggle": flip the bit at bit_index

Formal Specification

• Input:
  • register: integer
  • ops: list of [action, bit_index]
• Output:
  • Integer representing the final register value

Examples

Example 1

Input: register = 0, ops = [["set", 1], ["set", 3], ["toggle", 1]]
Output: 8

Explanation: 0 -> 2 -> 10 -> 8

Example 2

Input: register = 13, ops = [["clear", 2], ["toggle", 0]]
Output: 8

Explanation: 13 is 1101 in binary. Clearing bit 2 gives 1001 (9), then toggling bit 0 gives 1000 (8).

Constraints

• 0 <= register <= 10^9
• 1 <= len(ops) <= 10^5
• 0 <= bit_index <= 30
• Each action is one of "set", "clear", or "toggle"