
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
From an infinite arithmetic progression  $ 1,a_1,a_2,\dots$  of real numbers some terms are deleted, obtaining an infinite geometric progression  $ 1,b_1,b_2,\dots$  whose ratio is  $ q$ . Find all the possible values of  $ q$ .

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