import pandas as pd

def identify_segments(df):
    """
    Identify segments in a DataFrame based on conditions.

    Parameters:
    df (pd.DataFrame): The input DataFrame with conditions 'new_if_6_zero' and 'end_if_zero1'.

    Returns:
    valid_trigger (pd.Series): A boolean Series indicating which segments satisfy the conditions.
    outcome (pd.DataFrame): The segments that satisfy the conditions, indexed by 'x2' and 'x4'.
    """

    # Create columns 'x1', 'x2', 'x3', 'x4'
    df['x1'] = df['new_if_6_zero']==0
    df['x2'] = df['x1'].diff().fillna(True).cumsum()
    df['x3'] = (df['end_if_zero1']==0) & (df['end_if_zero2']==0)
    df['x4'] = df['x3'].diff().fillna(True).cumsum()

    # Create a boolean Series 'trigger' indicating which segments satisfy the conditions
    trigger = df.groupby(['x2', 'x4']).agg({'x1': 'sum', 'x3': 'any'}).rename(columns={'x1': 'start_trigger', 'x3': 'end_trigger'})
    valid_trigger = trigger[(trigger['start_trigger'].shift()>=6) & (trigger['end_trigger'].shift(-1))]

    # Create the segments that satisfy the conditions
    outcome = df.set_index(['x2', 'x4']).loc[valid_trigger.index]
    return valid_trigger, outcome

# Example usage:
df_example = pd.DataFrame({
    'new_if_6_zero': [0., 2, 0, 0, 0, 0, 0, 0, 3, 2, 4, 5],
    'end_if_zero1': [3., 0, 4, 5, 4, 3, 5, 6, 6, 1, 0, 2],
    'end_if_zero2': [3., 0, 4, 5, 4, 3, 5, 6, 6, 0, 0, 1]
})

valid_trigger, outcome = identify_segments(df_example)
print(valid_trigger)
print(outcome)