
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
There are grandmothers and grandfathers resting in the sanatorium, with the number of grandfathers being twice that of the grandmothers. The average age of the grandmothers is 5 years more, and the average age of all the pensioners is greater than 77 years but less than 78 years. Find the average age of the grandmothers, given that it is an integer number of years.

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