import numpy

def select_important_state():
    """
    Task-driven Hypothesis and Reasoning:
    ------------------------------------
    The environment involves two friendly center-back agents, two enemy players (goalkeeper and center-back),
    and the ball, all represented by absolute positions and directions.

    Since agents are center-backs (defenders), their main role is to:
    - Track their own positions and orientations (to maintain formation and coverage).
    - Monitor enemy attackers' (goalkeeper and center-back) positions and directions to anticipate threats.
    - Track the ball's position and direction, as it is the key object influencing the game state.

    Given partial observability and multi-agent coordination:
    - Own agents' absolute positions (s[0:4]) and directions (s[4:8]) are important for self-localization and coordination.
    - Enemy players' absolute positions (s[8:12]) and directions (s[12:16]) are critical for threat assessment.
    - Ball's absolute position (s[16:19]) and direction (s[19:22]) are essential for understanding play dynamics.

    Dimensions like absolute positions are harder to infer individually due to partial observability,
    so sharing these through communication is valuable for coordinated defense.

    Therefore, we prioritize:
    - Own agents' positions and directions: s[0:8]
    - Enemy players' positions and directions: s[8:16]
    - Ball position and direction: s[16:22]

    This covers all entities relevant to defensive coordination and task success.
    """

    important_dims = list(range(22))  # All dimensions since all contribute to coordination and situational awareness.
    return important_dims
