
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
Compute the sum of all positive integers  $a\leq 26$  for which there exist integers  $b$  and  $c$  such that  $a+23b+15c-2$  and  $2a+5b+14c-8$  are both multiples of  $26$ .

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