
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
The king distributed ducats to his sons. To the eldest son, he gave a certain number of ducats, to the younger son he gave one less ducat, and to the next younger son again one less ducat, and so he continued until the youngest. Then he returned to the eldest son and gave him one less ducat than the youngest received last time, and distributed in the same manner as in the first round. In this round, the youngest son received one ducat. The eldest son received a total of 21 ducats.

Determine how many sons the king had and the total number of ducats he distributed.

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