
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
Each of the number series a)-e) follows a certain pattern. Determine these patterns and write the next 2 numbers:

a) $19,20,22,25,29, \ldots$

b) $5,8,14,26,50, \ldots$

c) $253,238,223,208,193, \ldots$

d) $12,11,16,16,20,21,24,26, \ldots$

e) $15,29,56,109,214, \ldots$

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