
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
Mom baked a birthday cake for Ana, which weighs an integer number of grams. Before decorating it, she weighed the cake on a digital scale that rounds the weight to the nearest tens of grams (if the weight ends in 5, the scale rounds it down). The result was 1440 grams. After decorating the cake with candles, where the number of candles was equal to Ana's age, the scale showed 1610 grams. It is known that each candle weighs an integer number of grams, and if you place a single candle on the scale, it will show 40 grams. How old can Ana be? Provide all possible answers and explain why there are no other answers.

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