
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
Alex is given £1 by his grandfather and decides:
(i) to spend at least one third of £1 on toffees at 5 p each;
(ii) to spend at least one quarter of £1 on packs of bubblegum at 3 p each; and
(iii) to spend at least one tenth of £1 on jellybeans at 2 p each.
He only decides how to spend the rest of the money when he gets to the shop, but he spends all of the £1 on toffees, packs of bubblegum, and jellybeans.
What are the possibilities for the number of jellybeans that he buys?

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