
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
A wealthy senator in Ancient Rome left a will that stipulated the following distribution of his estate, which was worth 210 talents:

- If a son is born, he should receive two-thirds of the estate (140 talents), with the remaining one-third (70 talents) going to the mother.
- If a daughter is born, she should receive one-third of the estate (70 talents), with the remaining two-thirds (140 talents) going to the mother.

The senator's widow gave birth to twins: a boy and a girl. The will did not account for this possibility. How should the estate be divided among the three heirs to best approximate the conditions of the will?

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